Trigonometric Identities - ICSE STD 10 Mathematics Questions

Q 1[2 Mark Question Answer]2 Marks

$
\text { Prove that } \frac{\sin A}{\sin \left(90^{\circ}-A\right)}+\frac{\cos A}{\cos \left(90^{\circ}-A\right)}=\sec \left(90^{\circ}-A\right) \cos e c\left(90^{\circ}-A\right)
$

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Q 2[2 Mark Question Answer]2 Marks

Without using trigonometric identity, show that:
$
\sec 70^{\circ} \sin 20^{\circ}-\cos 20^{\circ} \cos e c 70^{\circ}=0
$

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Q 3[2 Mark Question Answer]2 Marks

Without using trigonometric identity, show that:
$
\cos ^2 25^{\circ}+\cos ^2 65^{\circ}=1
$

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Q 4[2 Mark Question Answer]2 Marks

Without using trigonometric identity, show that:
$
\sin \left(50^{\circ}+\theta\right)-\cos \left(40^{\circ}-\theta\right)=0
$

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Q 5[2 Mark Question Answer]2 Marks

Without using trigonometric identity, show that:
$
\tan 10^{\circ} \tan 20^{\circ} \tan 30^{\circ} \tan 70^{\circ} \tan 80^{\circ}=\frac{1}{\sqrt{3}}
$

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Q 6[3 marks sum]3 Marks

$
\text { Prove that } \sin \left(90^{\circ}-A\right) \cdot \cos \left(90^{\circ}-A\right)=\frac{\tan A}{1+\tan ^2 A}
$

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Q 7[3 marks sum]3 Marks

For $\triangle A B C$, prove that:
$
\sin \left(\frac{A+B}{2}\right)=\cos \frac{C}{2}
$

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Q 8[3 marks sum]3 Marks

For $\triangle A B C$, prove that :
$
\tan \left(\frac{B+C}{2}\right)=\cot \frac{A}{2}
$

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Q 9[3 marks sum]3 Marks

Find the value of $\theta\left(0^{\circ}<\theta<90^{\circ}\right)$ if :
$
\tan 35^{\circ} \cot \left(90^{\circ}-\theta\right)=1
$

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Q 10[3 marks sum]3 Marks

Without using trigonometric table, evaluate:
$
\left(\frac{\sin 47^{\circ}}{\cos 43^{\circ}}\right)^2-4 \cos ^2 45^{\circ}+\left(\frac{\cos 43^{\circ}}{\sin 47^{\circ}}\right)^2
$

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Q 11[5 marks sum]5 Marks

Prove the following identity :
$
\frac{\cot ^2 \theta(\sec \theta-1)}{(1+\sin \theta)}=\sec ^2 \theta\left(\frac{1-\sin \theta}{1+\sec \theta}\right)
$

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Q 12[5 marks sum]5 Marks

Prove the following identity :
$
\left[\frac{1}{\left(\sec ^2 \theta-\cos ^2 \theta\right)}+\frac{1}{\left(\operatorname{cosec} 2-\sin ^2 \theta\right)}\right]\left(\sin ^2 \theta \cos ^2 \theta\right)=\frac{1-\sin ^2 \theta \cos ^2 \theta}{2+\sin ^2 \theta \cos ^2 \theta}
$

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Q 13[5 marks sum]5 Marks

Prove the following identity:
$
\frac{\cos ^3 \theta+\sin ^3 \theta}{\cos \theta+\sin \theta}+\frac{\cos ^3 \theta-\sin ^3 \theta}{\cos \theta-\sin \theta}=2
$

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Q 14[5 marks sum]5 Marks

Prove the following identity:
$
\frac{\cos ^3 A+\sin ^3 A}{\cos A+\sin A}+\frac{\cos ^3 A-\sin ^3 A}{\cos A-\sin A}=2
$

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Q 15[4 marks sum]4 Marks

$
\text { Given } \cos 38^{\circ} \sec \left(90^{\circ}-2 A\right)=1 \text {, Find the value of } \angle \mathrm{A}
$

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Q 16[4 marks sum]4 Marks

$
\text { Find } x \text {, if } \cos (2 x-6)=\cos ^2 30^{\circ}-\cos ^2 60^{\circ}
$

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Q 17[4 marks sum]4 Marks

$
\text { Find the value of } \mathrm{x} \text {, if } \cos x=\cos 60^{\circ} \cos 30^{\circ}-\sin 60^{\circ} \sin 30^{\circ}
$

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Q 18[4 marks sum]4 Marks

$
\text { If } \tan A+\sin A=m \text { and } \tan A-\sin A=n \text {, prove that }\left(m^2-n^2\right)^2=16 m n
$

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Q 19[4 marks sum]4 Marks

$
\text { If } \frac{x}{a \cos \theta}=\frac{y}{b \sin \theta} \text { and } \frac{a x}{\cos \theta}-\frac{b y}{\sin \theta}=a^2-b^2, \text { prove that } \frac{x^2}{a^2}+\frac{y^2}{b^2}=1
$

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Trigonometric Identities question types

Trigonometric Identities questions

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Trigonometric Identities Mathematics - Trigonometric Identities

Trigonometric Identities question types

Trigonometric Identities questions

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