In LHS we need to convert cotsup2sup A in terms of tansup2sup A for second term

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

Question 29 Trigonometric Identities Exercise 18

$\frac{\tan ^{2} A}{1+\tan ^{2} A}+\frac{\cot ^{2} A}{1+\cot ^{2} A}=1$

Answer:

In LHS, we need to convert cot² A in terms of tan² A for second term.

$\begin{aligned} &\text { L.H.S. }=\frac{\tan ^{2} A}{1+\tan ^{2} A}+\frac{\frac{1}{\tan ^{2} A}}{1+\frac{1}{\tan ^{2} A}}\\ &=\frac{\tan ^{2} A}{1+\tan ^{2} A}+\frac{\frac{1}{\tan ^{2} A}}{\frac{\tan ^{2} A+1}{\tan ^{2} A}}\\ &=\frac{\tan ^{2} A}{1+\tan ^{2} A}+\frac{\tan ^{2} A}{\tan ^{2} A\left(\tan ^{2} A+1\right)}\\ &=\frac{\tan ^{2} A}{1+\tan ^{2} A}+\frac{1}{1+\tan ^{2} A}\\ &=\frac{1+\tan ^{2} \mathrm{~A}}{1+\tan ^{2} \mathrm{~A}}=1=\mathrm{R} . \mathrm{H} . \mathrm{S} . \end{aligned}$

Related Questions

If A is an acute angle and sin A = 3/5, find all other trigonometric ratios of angle A (using trigon...

If A is an acute angle and sec A = 17/8, find all other trigonometric ratios of angle A (using trigo...

Express the ratios cos A, tan A and sec A in terms of sin A.

cos2 26o + cos 64o sin 26o + (tan 36o/ cot 54...

(sec 17o/ cosec 73o) + (tan 68o/ cot 22o) + cos2</s...

(sin 65o/ cos 25o) + (cos 32o/sin 58o) – sin 28o</s...