Question

(1 + tan^2 theta)( 1 + 1/tan^2 theta) = 1/sin^2 theta - sin^4 theta1

Answer 1

Answer:

$(1+tan^{2}\theta)(1+\frac{1}{tan^{2}\theta})=\frac{1}{sin^{2}\theta-sin^{4}\theta}$

Step-by-step explanation:

$LHS=(1+tan^{2}\theta)(1+\frac{1}{tan^{2}\theta})$

$=sec^{2}\theta (1+cot^{2}\theta)\\=sec^{2}\theta cosec^{2}\theta\\=\frac{1}{cos^{2}\theta} \times \frac{1}{sin^{2}\theta}\\=\frac{1}{(1-sin^{2}\theta)sin^{2}\theta}\\=\frac{1}{sin^{2}\theta-sin^{4}\theta}\\=RHS$

Therefore,

$(1+tan^{2}\theta)(1+\frac{1}{tan^{2}\theta})=\frac{1}{sin^{2}\theta-sin^{4}\theta}$

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Answer 2

Answer:

Step-by-step explanation: