Trigonometric Identities - Gujarat Board (GSEB) STD 10 Maths Questions

Very-Short and Short-Answer Questions.
If $5\text{x}=\sec\theta$ and $\frac{5}{\text{x}}=\tan\theta,$ find the value of $5\Big(\text{x}^2-\frac{1}{\text{x}^2}\Big).$

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Q 123 Marks Question3 Marks

Prove the following identities:
$\frac{1-\tan^2\theta}{\cot^2-1}=\tan^2\theta$

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Q 133 Marks Question3 Marks

Very-Short and Short-Answer Qustions:
Write the value of $\big(1+\tan^2\theta\big)\big(1+\sin\theta\big)\big(1-\sin\theta\big).$

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Q 143 Marks Question3 Marks

Prove the following identities:
$\frac{\cos\theta}{(1-\tan\theta)}+\frac{\sin^2\theta}{(\cos\theta-\sin\theta)}=(\cos\theta+\sin\theta)$

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Q 153 Marks Question3 Marks

Prove the following identities:
$1+\frac{\tan^2\theta}{(1+\sec\theta)}=\sec\theta$

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Q 164 Marks Questions4 Marks

Prove the following identities:
$\frac{\tan\theta}{(\sec\theta-1)}+\frac{\tan\theta}{(\sec\theta+1)}=2\text{cosec}\theta$

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Q 174 Marks Questions4 Marks

Prove the following identities:
$(1+\tan\theta+\cot\theta)(\sin\theta-\cos\theta)=\Big(\frac{\sec\theta}{\text{cosec}^2\theta}-\frac{\text{cosec}\theta}{\sec^2\theta}\Big)$

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Q 184 Marks Questions4 Marks

Prove the following identities:
If $1+\sin^2\theta=3\sin\theta\cos\theta$ then prove that $\tan\theta=1$ or $\frac12.$

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Q 194 Marks Questions4 Marks

Prove the following identities:
$\frac{1-\tan^2\theta}{1+\tan^2\theta}=\big(\cos^2\theta-\sin^2\theta\big)$

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Q 204 Marks Questions4 Marks

Prove the following identities:
$\frac{\sec\theta-\tan\theta}{\sec\theta+\tan\theta}=\frac{\sin^2\theta}{(1+\cos\theta)^2}$

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