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Trigonometrical Ratios, Functions and Identities question bank (Mathematics)

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Q1.

If $\cos(\theta - \alpha) = a$ and $\sin(\theta - \beta) = b$, then the value of $\cos^2(\alpha - \beta) + 2ab \sin(\alpha - \beta) + \cos^2(\theta - \alpha)$ is...

(A)

$a^2 + b^2$

(B)

$a^2 - b^2$

(C)

$b^2 - a^2$

(D)

$a^2 + 2b^2$

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Q2.

The value of the expression $\sqrt{3} \operatorname{cosec} 20^{\circ}-\sec 20^{\circ}$ is equal to

(A)

$2$

(B)

$\frac{2 \sin 20^{\circ}}{\sin 40^{\circ}}$

(C)

$4$

(D)

$4 \frac{\sin 20^{\circ}}{\sin 40^{\circ}}$

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