Question

if √3 tan a =1 then find the value of sin square A -cos square A

Answer 1

Heya Friend ☺

Given ✓3 tanA=1

To find:- sin²A-cos²A

Solution:-
$tan \: a = \frac{1}{ \sqrt{3} } \\ tan \: a = tan \: 30 \\ a = {30}^{}$
Now putting value in sin and cos

${sin}^{2} 30 + {cos}^{2} 30 \\ = 1$
because it's an identity that sin²Q+ cos²Q=1

Answer 2

root 3 tanA = 1

tan A = 1/root 3

tan 30 = 1/root 3

sin^A - cos^A = sin^30 - cos^30

= (1/2)^ - (root 3/2)^

= 1/4 -3/4 = 2/4 = 1/2