Question

Prove the Identity :-


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Answer 1

it's solution is given in the attachment pls mark it brainliest

Answer 2

$\boxed{\underline{\textsf{What is trigonometry?}}}$

$\textsf{Trigonometry is the study of angles}$
$\textsf{and its sine, cosine, tangent, cosectant,}$
$\textsf{sectant and cotangent ratios.}$

$1.\:sin\theta * cosec\theta= 1$

$2.\:cos\theta * sec\theta = 1$

$3.\:tan\theta * cot\theta = 1$

$4.\:sin^{2}\theta + cos^{2}\theta = 1$

$5.\:sec^{2}\theta - tan^{2}\theta = 1$

$6.\:cosec^{2}\theta - cot^{2}\theta = 1$

$\boxed{\underline{\textsf{Solution :}}}$

$\textsf{Now,}\:\dfrac{sinx-tanx}{sinx*tanx}$

$=\dfrac{sinx-\dfrac{sinx}{cosx}}{sinx*\dfrac{sinx}{cosx}}$

$\textsf{since}\:tanx=\dfrac{sinx}{cosx}$

$=\dfrac{sinx*\bigg(1-\dfrac{1}{cosx}\bigg)}{sinx*\dfrac{sinx}{cosx}}$

$=\dfrac{1-\dfrac{1}{cosx}}{\dfrac{sinx}{cosx}}$

$=\dfrac{\dfrac{cosx-1}{cosx}}{\dfrac{sinx}{cosx}}$

$=\dfrac{cosx-1}{sinx}$

$\to \boxed{\dfrac{sinx-tanx}{sinx*tanx}=\dfrac{cosx-1}{sinx}}$

$\textsf{Hence, proved.}$