Question

If sinθ=cosθ,find the value of 2tanθ+cos²θ.​

Answer 1

Answer:

$\sin( \alpha ) = \cos( \alpha ) \\ hence \: \\ 2 \tan( \alpha ) + { \cos( \alpha ) }^{2} = 2 \frac{ \sin( \alpha ) }{ \cos( \alpha ) } + { \cos( \alpha ) }^{2} \\ 2 \frac{ \cos( \alpha ) }{ \cos( \alpha ) } + { \cos( \alpha ) }^{2} \\ = 2 + { \cos( \alpha ) }^{2}$

Answer 2

$\bold{\huge{\underline{\underline{\rm{ Given :}}}}}$

$sin \: \theta = \cos\theta$

$\bold{\huge{\underline{\underline{\rm{ To\:Find :}}}}}$

The value of

$2tan\theta + {cos}^{2} \theta$

$\huge{\underline{\underline{\red{Solution→}}}}$

$= 2tan\theta + {cos}^{2} \theta \:$

We know that -

• ${tan\theta} = \frac{sin\theta}{cos \: \theta}$

$= 2 \times \frac{sin \:\theta }{cos \: \theta} + {cos}^{2} \theta$

But

$sin \: \theta = cos \: \theta$

(Given)

$= 2 \times \frac{cos \:\theta }{cos \: \theta} + {cos}^{2} \theta$

$= 2 + {cos}^{2} \theta$

$\rule{200}{1}$

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