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)



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.


\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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