Question

Please help prove both the sides equal​

Answer 1

LHS =

(sin . cos ) + sin²

tan

= (sin . cos) ÷ sin + sin²

cos

= (sin . cos) x cos + sin²

sin

= cos² + sin²

= 1

= RHS

Brainliest to banta hai

Answer 2

Question:

Prove that ${\sf{\ \ {\dfrac{sin \theta cos \theta}{tan \theta}} + sin^2 \theta = 1}}$

Step-by-step explanation:

To Prove : ${\sf{\ \ {\dfrac{sin \theta cos \theta}{tan \theta}} + sin^2 \theta = 1}}$

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Solution :

L.H.S. = ${\sf{\ \ {\dfrac{sin \theta cos \theta}{tan \theta}} + sin^2 \theta}}$

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${\boxed{\tt{Identity \ : \ tan \theta = {\dfrac{sin \theta}{cos \theta}} }}}$

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$\implies{\sf{ {\dfrac{sin \theta cos \theta}{ {\dfrac{sin \theta}{cos \theta}} }} + sin^2 \theta}}$

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$\implies{\sf{ sin \theta cos \theta \times {\dfrac{cos \theta}{sin \theta}} + sin^2 \theta}}$

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$\implies{\sf{ cos \theta \times cos \theta + sin^2 \theta}}$

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$\implies{\sf{cos^2 \theta + sin^2 \theta}}$

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${\boxed{\tt{Identity \ : \ sin^2 \theta + cos^2 \theta = 1}}}$

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$\implies{\boxed{\sf{1}}}$

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= R.H.S.

Hence, proved !!