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If {}={2x(x+1)}{2x+1}, find {}

Question

If $tan θ = \frac{2 x ( x + 1 )}{2 x + 1}$ , find $sin θ$

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Jack Discussed

If

tan θ = \frac{2 x ( x + 1 )}{2 x + 1}

, find

sin θ

13 mins ago

Discuss this question LIVE

13 mins ago

Text solutionVerified

t an θ = \frac{2 x ( x + 1 )}{2 x + 1}

,

se c^{2} θ = 1 + t a n^{2} θ

=

1 + \frac{( 2 x ( x + 1 ) ) ^{2}}{( 2 x + 1 ) ^{2}}

=

\frac{( 2 x + 1 ) ^{2} + 4 x ^{2} ( x + 1 ) ^{2}}{( 2 x + 1 ) ^{2}}

=

\frac{( 2 x ^{2} + 2 x + 1 ) ^{2}}{( 2 x + 1 ) ^{2}}

and

sec θ = \frac{( 2 x ^{2} + 2 x + 1 )}{( 2 x + 1 )}

,

cos θ = \frac{( 2 x + 1 )}{( 2 x ^{2} + 2 x + 1 )}

, We have

s i n^{2} θ = 1 - co s^{2} θ

=

1 - (\frac{( 2 x + 1 )}{( 2 x ^{2} + 2 x + 1 )})^{2}

= \frac{( 2 x ^{2} + 2 x + 1 ) ^{2} - ( 2 x + 1 ) ^{2}}{( 2 x ^{2} + 2 x + 1 ) ^{2}}

using

a^{2} - b^{2} = (a + b) (a - b)

= \frac{( x ^{2} + 2 x + 1 ) ( 4 x ^{2} )}{( 2 x ^{2} + 2 x + 1 ) ^{2}}

and this gives

s in θ = \frac{( x + 1 ) ( 2 x )}{( 2 x ^{2} + 2 x + 1 )}

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Question Text	If $tan θ = \frac{2 x ( x + 1 )}{2 x + 1}$ , find $sin θ$
Answer Type	Text solution:1
Upvotes	151