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if tan a 3/4 then prove that sinA cosA 12/25

Posted by Shiv Dubey 6 years, 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 4 months ago

Given, tan A = {tex}\frac { 3 } { 4 }{/tex}

⇒ tan A = {tex}\frac { P } { B } = \frac { 3 x } { 4 x }{/tex} [ from figure ]

H² = P² + B² [By Pythagoras theorem]
= (3x)² + (4x)²
= 9x² + 16x²

⇒ H² = 25x²

or, H²=(5x)²

⇒ H = 5x

Therefore,

sin A = {tex}\frac { P } { H } = \frac { 3 x } { 5 x } = \frac { 3 } { 5 }{/tex}

and cos A = {tex}\frac { B } { H } = \frac { 4 x } { 5 x } = \frac { 4 } { 5 }{/tex}

Now, LHS = sin A cos A

{tex}= \frac { 3 } { 5 } \times \frac { 4 } { 5 } = \frac { 12 } { 25 }{/tex} = RHS

Hence, proved.

0Thank You

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