How i solve the ncert class 10 introduction of trigonometry question of exercise 8.1 question no.8 , this question is very hard to solve . Sir please help me to solve this question because i can’t solve this question properly .If 3 cot A = 4, check whether (1-tan2 A)/(1+tan2 A) = cos2 A – sin 2 A or not.

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Let △ABC in which ∠B=90°

We know that, cot function is the reciprocal of tan function and it is written as

cot(A) = AB/BC = 4/3

Let AB = 4k an BC =3k, where k is a positive real number.

According to the Pythagorean theorem,

AC

^{2}=AB^{2}+BC^{2}AC

^{2}=(4k)^{2}+(3k)^{2}AC

^{2}=16k^{2}+9k^{2}AC

^{2}=25k^{2}AC=5k

Now, apply the values corresponding to the ratios

tan(A) = BC/AB = 3/4

sin (A) = BC/AC = 3/5

cos (A) = AB/AC = 4/5

Now compare the left hand side(LHS) with right hand side(RHS)

Since, both the LHS and RHS = 7/25

R.H.S. =L.H.S.

Hence,

(1-tanis proved^{2 }A)/(1+tan^{2}A) = cos^{2}A – sin^{2 }A