Question

What-is-the-value-of-tan-theta-if-sin-theta+cos-theta=√2-cos-theta​

Answer 1

sinθ+cosθ=√2-cosθ

Dividing both side by cosθ,

tanθ+1=√2secθ-1

tanθ+2=√2secθ

Squaring both sides,

(tanθ+2)²=2sec²θ

tan²θ+4tanθ+4=2(1+tan²θ)

tan²θ+4tanθ+4=2+2tan²θ

tan²θ-4tanθ-2=0

(tanθ-2)²-6=0

(tanθ-2)²=6

tanθ-2=√6

tanθ=±√6+2