Pl solve : tan(2 tan^-1 (1/5) - π/4)
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Let tan ^ -1 (1/5) = X.
Then , tan X = 1/5
Now , tan (2X-π/4) = { tan(2X) - tan(π/4) } / 1+ tan(2X)tan(π/4)
Since, tan(π/4) = 1
tan (2X-π/4) = tan(2X) / 1 + tan(2X)
= 2tanX /( 1 - tan^2X + 2tanX )
= 2 × 1/5 / ( 1 - 1/25 + 2 × 1/5 )
= (2/5) /{ (25-1+10) / 25}
= (2/5) / (34/25)
= 5/17
Then , tan X = 1/5
Now , tan (2X-π/4) = { tan(2X) - tan(π/4) } / 1+ tan(2X)tan(π/4)
Since, tan(π/4) = 1
tan (2X-π/4) = tan(2X) / 1 + tan(2X)
= 2tanX /( 1 - tan^2X + 2tanX )
= 2 × 1/5 / ( 1 - 1/25 + 2 × 1/5 )
= (2/5) /{ (25-1+10) / 25}
= (2/5) / (34/25)
= 5/17
Swapnil1234:
But ans. Is -7/17
Ok
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9
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