cos(2tan−171)−sin(4tan−131)=

cos(2tan−171 ) −sin(4tan−131 ) Take 2tan−171= y then tan y/2=71hence siny/2=501 and cosy/2=507Therefore , siny =2(cos y/2)(sin y/2)=507×501=257 =cos(sin−1257 ) −sin(sin−12524 ) =cos(cos−12524 ) −sin(sin−12524 ) =2524−2524=0

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{ ( 2 {^{-1} {1}{7}} )} - { ( 4 {^{-1} {1}{3}} )} =

Question

$cos (2 tan^{- 1} \frac{1}{7}) - sin (4 tan^{- 1} \frac{1}{3}) =$

1

\frac{1}{2}

- \frac{1}{2}

0

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Text solutionVerified

cos (2 tan^{- 1} \frac{1}{7}) - sin (4 tan^{- 1} \frac{1}{3})

Take

2 tan^{- 1} \frac{1}{7} = y

then

tan y /2 = \frac{1}{7}

hence

sin y /2 = \frac{1}{50}

and

cos y /2 = \frac{7}{50}

Therefore ,

s in y = 2 (cos y /2) (s in y /2) = \frac{7}{50} \times \frac{1}{50} = \frac{7}{25}

= cos (sin^{- 1} \frac{7}{25}) - sin (sin^{- 1} \frac{24}{25})

= cos (cos^{- 1} \frac{24}{25}) - sin (sin^{- 1} \frac{24}{25})

= \frac{24}{25} - \frac{24}{25} = 0

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Question Text	$cos (2 tan^{- 1} \frac{1}{7}) - sin (4 tan^{- 1} \frac{1}{3}) =$
Answer Type	Text solution:1
Upvotes	150

cos(2tan−171​)−sin(4tan−131​)=

Text solutionVerified

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