ML Aggarwal Solutions Class 10 Mathematics Solutions for Trigonometric Identities Exercise 18 in Chapter 18 - Trigonometric Identities

Question 8 Trigonometric Identities Exercise 18

(sin 35o cos 55o + cos 35o sin 55 o)/ (cosec2 10o – tan2 80 o)

Solution:

In trigonometry, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined.

Given,

\begin{aligned} &=\frac{\sin 35^{\circ} \cos \left(90^{\circ}-35^{\circ}\right)+\cos 35^{\circ} \sin \left(90^{\circ}-35^{\circ}\right)}{\operatorname{cosec}^{2} 10^{\circ}-\tan ^{2}\left(90^{\circ}-10^{\circ}\right)} \\ &=\frac{\sin 35^{\circ} \sin 35^{\circ}+\cos 35^{\circ} \cos 35^{\circ}}{\operatorname{cosec}^{2} 10^{\circ}-\cot ^{2} 10^{\circ}} \\ &=\frac{\sin ^{2} 35^{\circ}+\cos ^{2} 35^{\circ}}{\operatorname{cosec}^{2} 10^{\circ}-\cot ^{2} 10^{\circ}}=\frac{1}{1}=1 \end{aligned}

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