Question

1
Prove that (1+tan^2 theta) +[1+1/tan^2theta]=1/sin^2theta-sin^4theta​

Answer 1

Step-by-step explanation:

(1 + tan²θ) + (1 + 1/tan²θ)

sec²θ + cosec²θ

$\frac{1}{cos^{2} }$ + $\frac{1}{sin^{2} }$  

$\frac{sin^{2} + cos ^{2} }{sin^{2} cos^{2} }$ = $\frac{1}{sin^{2} (1 - sin^{2}) }$

$\frac{1}{sin^{2} -sin^{4}}$

L.H.S = R.H.S

Hence proved

[1 + tan²θ = sec²θ , 1 + 1/tan²θ  = cosec²θ , 1- sin²= cos², sin²+cos² = 1]

Answer 2

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