Find the value of the following-tan -1-2 cos2 sin -11-2-

Tan^ 1 [ 2cos ( 2sin^ 11/2 ) ]=tan^ 1 [ 2cos{ 2sin^ 1 ( sinπ/6 ) } ] ( ∵ sinπ/6=1/2 ) =tan^ 1 [ 2cos ( 2×π/6 ) ]=tan^ 1 [ 2cosπ/3 ] =tan^ 1 [ 2×1/2 ]=tan^ ...

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Standard XII

Mathematics

Sign of Trigonometric Ratios in Different Quadrants

Find the valu...

Question

Find the value of the following:

$t a n^{- 1} [2 c o s (2 s i n^{- 1} \frac{1}{2})]$

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Solution

$t a n^{- 1} [2 c o s (2 s i n^{- 1} \frac{1}{2})] = t a n^{- 1} [2 c o s {2 s i n^{- 1} (s i n \frac{π}{6})}] (∵ s i n \frac{π}{6} = \frac{1}{2}) = t a n^{- 1} [2 c o s (2 \times \frac{π}{6})] = t a n^{- 1} [2 c o s \frac{π}{3}] = t a n^{- 1} [2 \times \frac{1}{2}] = t a n^{- 1} (1) (∵ c o s \frac{π}{3} = \frac{1}{2}) = t a n^{- 1} (t a n \frac{π}{4}) = \frac{π}{4}$

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Find the value of the following: tan−1[2cos(2sin−112)]

tan−1[2cos(2sin−112)]=tan−1[2cos{2sin−1(sinπ6)}](∵ sinπ6=12)=tan−1[2cos(2×π6)]=tan−1[2cosπ3]=tan−1[2×12]=tan−1(1) (∵cos π3=12)=tan−1(tanπ4)=π4

Find the value of the following:

$t a n^{- 1} [2 c o s (2 s i n^{- 1} \frac{1}{2})]$