Question

show that (sin theta+cos theta)^2+(cos theta+sec theta)^2=7+tan^2 theta + cot^2 thet​

Answer 1

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$\huge\mathbb\red{Solution:-}$

  To prove:

(sinθ+cosecθ)²+(cosθ+secθ)²=7+tan²θ+cot²θ

L.H.S. =(sinθ+cosecθ)²+(cosθ+secθ)²

=sin²+cosec²θ+2sinθ.cosecθ+cos²θ+2+1+tan²θ+2

=1+6+tan²θ+cot²θ

=7+tan² θ+cot² θ

 = R.H.S. $.$