Question

if root 3 tan theta is equal to 3 sin theta and find the value of sin square theta minus cos square theta

Answer 1

√3 tanA=3sinA
√3sinA/√3cosA=√3×√3 sinA
1/√3sinA=√3
1=3sinA
sinA=1/3
=>sin²A=1/9
=>cos²A=8/9

So, sin²A-cos²A=(1/9)-(8/9)
=-7/9

Answer 2

3tanA = 3sinA (given)
3sinA/cosA = 3sinA
1/cosA= 1
therefore, cosA = 1. ....(1)

to find:- sin^2A - cos^2A
=(1-cos^2A)-cos^2A
=1- 2cos^2A
therefore, 1 - 2(1). from eq. (1)
=1-2
=-1