Question

cos θ (1 + tan θ) = 1​

Answer 1

$\huge\underline\mathfrak\purple{♡ Answer ♡}$

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L.H.S.$\frac{cos\theta}{-1\tan\theta}+\frac{sin\theta}{1-\cot\theta}$

= $\frac{cos\theta}{1-sin\theta}{cos\theta}$

= $\frac{cos^2\theta}{cos\theta}{-sin\theta}$

Taking LCM ,we get

$\frac{cos\theta-sin^2\theta}{\{cos\theta-sin\theta}$

Using identity, a²-b² =(a+b)(a-b)we have

=$\frac{(cos\theta-sin\theta}{(cos\theta +sin\theta)}$

= $\frac{cos\theta+sin\theta}$ = RHS

Hence proved

Hope it's helps you ☺️