Math, asked by Nandukkn7046780, 9 months ago

(sina- coseca)(cosa-seca)=1/tana+cota

Answers

Answered by brainlyaryan12

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$\huge{\orange{\fbox{\fbox{\blue{\bigstar{\mathfrak{\red{Answer}}}}}}}}$

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$(Sin \theta- Cosec)(Cos-sec) = \frac{1}{Tan+Cot}$

On solving LHS

=> $(Sin \theta - \frac{1}{Sin})(Cos \theta - \frac{1}{Cos})$

=> $(\frac{Sin^2 - 1}{Sin})(\frac{Cos^2 -1}{Cos})$

=> $(\frac{-Cos^2}{Sin})(\frac{-Sin^2}{Cos})$

=> $(\frac{-Cos^2}{Sin} × \frac{-Sin^2}{Cos})$

=> $(-Cos×-Sin)$

=> $(Cos.Sin)$

On solving RHS

$\frac{1}{Tan + Cot}$

=> $\frac{1}{\frac{Sin}{Cos} + \frac{Cos}{Sin}}$

=> $\frac{1}{\frac{Sin^2+Cos^2}{Sin.Cos}}$

=> $\frac{Sin.Cos}{Sin^2+Cos^2}$

=> $\frac{Sin.Cos}{1}$

=> $Sin.Cos$

$\huge\orange{\fbox{\pink{\text{LHS=RHS }}}}$

$\huge{\purple{\bigstar{\blue{\text{Hope it helps...}}}}}$

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