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

Question 10 Trigonometric Identities Exercise 18

(tan 25o/ cosec 65o)2 + (cot 25o/ sec 65o)2 + 2 tan 18o tan 45o tan 75o

Solution:

Trigonometric identities are equalities in trigonometry that use trigonometric functions and are valid for any value of the variables that occur and are specified on both sides of the equality.

\begin{aligned} &=\left(\frac{\tan 25^{\circ}}{\operatorname{cosec}\left(90^{\circ}-25^{\circ}\right)}\right)^{2}+\left(\frac{\cot 25^{\circ}}{\sec \left(90^{\circ}-25^{\circ}\right)}\right)^{2}+2 \tan 18^{\circ} \tan \left(90^{\circ}-18^{\circ}\right) \tan 45^{\circ} \\ &=\left(\frac{\tan 25^{\circ}}{\sec 25^{\circ}}\right)^{2}+\left(\frac{\cot 25^{\circ}}{\operatorname{cosec} 25^{\circ}}\right)^{2}+2 \tan 18^{\circ} \cot 18^{\circ} \tan 45^{\circ} \\ &=\left(\frac{\sin 25^{\circ} \times \cos 25^{\circ}}{\cos 25^{\circ} \times 1}\right)^{2}+\left(\frac{\cos 25^{\circ} \times \sin 25^{\circ}}{\sin 25^{\circ} \times 1}\right)+2 \times 1 \times 1 \quad\left\{\because \sin ^{2} \theta+\cos ^{2} \theta=1\right\} \\ &=\tan \theta \cot \theta=1 \end{aligned}

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