Math, asked by advanced3, 3 months ago

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Answered by BrainlyEmpire
48

✮ Question ✮

\sf{Prove\:that\:tan^2\theta-sin^2\theta=tan^2\theta\:sin^2\theta}

✮ Identities Used ✮

\sf{1-cos^2\theta=sin^2\theta}\\\sf{\dfrac{sin\theta}{cos\theta}=tan\theta}

✮ Solution ✮

\sf{Taking\:L.H.S,}

\sf{tan^2\theta-sin^2\theta}

\sf{\dfrac{sin^2\theta}{cos^2\theta}-sin^2\theta}

\sf{\dfrac{sin^2\theta-sin^2\theta\:cos^2\theta}{cos^2\theta}}

\sf{Taking\:sin^2\theta\:as\:common}

\sf{\dfrac{sin^2\theta\left(1-cos^2\theta\right)}{cos^2\theta}}

\sf{\dfrac{sin^2\theta}{cos^2\theta}sin^2\theta}

\boxed{\sf{\tan^2\theta\:sin^2\theta}}

\sf{L.H.S=R.H.S}

\sf{\mathrm{HENCE\:PROVED}}

Answered by ItzMiracle
101

\huge\underbrace\mathrm\purple{Answer}

\sf{Taking\:L.H.S,}

\sf{tan^2\theta-sin^2\theta}

\sf{\dfrac{sin^2\theta}{cos^2\theta}-sin^2\theta}

\sf{\dfrac{sin^2\theta-sin^2\theta\:cos^2\theta}{cos^2\theta}}

\sf{Taking\:sin^2\theta\:as\:common}

\sf{\dfrac{sin^2\theta\left(1-cos^2\theta\right)}{cos^2\theta}}

\sf{\dfrac{sin^2\theta}{cos^2\theta}sin^2\theta}

\boxed{\sf{\tan^2\theta\:sin^2\theta}}

\sf{L.H.S=R.H.S}

\sf{\mathrm{HENCE\:PROVED}}

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