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Trigonometrical Identities Mathematics - Trigonometrical Identities

ICSE - STD 10 - Mathematics (ICSE - English Medium). 362 questions in this chapter.

Question types

Trigonometrical Identities question types

362 questions across 5 question groups — pick any mix to generate a Mathematics paper with step-by-step answer keys.

362
Questions
5
Question groups
5
Question types
Sample Questions

Trigonometrical Identities questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 4[1 Mark Question Answer]1 Mark
Evaluate
$2\left(\frac{\tan 35^{\circ}}{\cot 55^{\circ}}\right)+\left(\frac{\cot 55^{\circ}}{\tan 35^{\circ}}\right)-3\left(\frac{\sec 40^{\circ}}{\cos e c 50^{\circ}}\right)$
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Q 12[3 marks sum]3 Marks
Prove that:
$\frac{1}{1+\sin \left(90^{\circ}-A\right)}+\frac{1}{1-\sin \left(90^{\circ}-A\right)}=2 \sec ^2\left(90^{\circ}-A\right)$
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Q 13[3 marks sum]3 Marks
Prove that:
$\frac{1}{1+\cos \left(90^{\circ}-A\right)}+\frac{1}{1-\cos \left(90^{\circ}-A\right)}=2 \operatorname{cosec} 2\left(90^{\circ}-A\right)$
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Q 16[5 marks sum]5 Marks
If A and B are complementary angles, prove that:$\frac{\sin A+\sin B}{\sin A-\sin B}+\frac{\cos B-\cos A}{\cos B+\cos A}=\frac{2}{2 \sin ^2 A-1}$
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Q 18[5 marks sum]5 Marks
Prove the following identitie:
$\cot ^2 A\left(\frac{\sec A-1}{1+\sin A}\right)+\sec ^2 A\left(\frac{\sin A-1}{1+\sec A}\right)=0$
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Q 20[5 marks sum]5 Marks
Prove that
$\cot ^2 A-\cot ^2 B=\frac{\cos ^2 A-\cos ^2 B}{\sin ^2 A \sin ^2 B}=\operatorname{cosec}{ }^2 A-\operatorname{cosec} B$
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