Question

1+sin^2θ -3sinθ cosθ prove that tanθ =1

Answer 1

Answer:

1+sin^2θ -3sinθ cosθ

= (sin^2θ +cos^2θ) + sin^2θ -3sinθ cosθ = 0

= sin^2θ + cos^2θ + sin^2θ = 3sinθ cosθ

= (sin^2θ + cos^2θ + 2sinθ cosθ) + sin^2θ = 3sinθ cosθ + 2sinθ cosθ

= (sinθ + cosθ)^2 + sin^2θ = 5sinθ cosθ

= sinθ + cosθ + tan θ = 5

tanθ = 5 - (sinθ+ cosθ)

If sinθ+ cosθ = 4

then tan θ = 5-4

tanθ = 1

Not enough information in question.

I have attached one link it is same question but not this answer, it's another one written by someone but it might be helpful

https://www.sarthaks.com/930705/if-1-sin-2-3-sin-cos-then-prove-that-tan-1-or-1-2