Question

if 3 cotA =4 then find wheather 1-sin^2A /1+sin^2 A. = cos^2 A - sin^2 are equal or not... ​

Answer 1

Answer:

they're not equal

Step-by-step explanation:

3 cotA = 4

=> cot A = 4/3

cot = adjacent side / opposite side

=> adjacent side = 4x and opposite side = 3x

By Pythagoras theorem we get

(hypotenuse)^2 = opposite side^2 + adjacent side^2

=> hypotenuse^2 = 9x^2 + 16x^2,on solving

=> hypotenuse = 5x

Now

sin A = opposite / hypotenuse

= 3x/5x = 3/5

cos A = adjacent / hypotenuse

= 4x/5x = 4/5

ATQ;

1 - sin^2 A/1 + sin^2 A

= 1 - (3/5)^2/1 + (3/5)^2

= (1 - 9/25) / 1 + 9/25

=( 16/25) / (34/25)

= 16/34

= 8/17

cos^2 A - sin^2 A

= (4/5)^2 - (3/5)^2

= 16/25 - 9/25

= 7/25

8/17 is not equal is not equal to 7/25