Let 0≤ x ≤π So, cos^ 14/5=x⇒ cos x=4/5 ....(i) Now sin ( 1/2cos^ 14/5 )=sin ( x/2 ) ....(ii) From (i), cos x=4/5⇒ 1 2 sin^2x/2=4/5 ⇒ 2 sin^2x/2=1 4/5=1/ ...

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Byju's Answer

Standard XIII

Mathematics

Properties Derived from Trigonometric Identities

sin 1/2cos-14...

Question

$s i n (\frac{1}{2} c o s^{- 1} \frac{4}{5}) =$

\frac{1}{\sqrt{10}}

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- \frac{1}{\sqrt{10}}

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\frac{1}{10}

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- \frac{1}{10}

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Solution

The correct option is A $\frac{1}{\sqrt{10}}$
Let $0 \leq x \leq π$
So, $c o s^{- 1} \frac{4}{5} = x \Rightarrow c o s x = \frac{4}{5}$ ....(i)
Now $s i n (\frac{1}{2} c o s^{- 1} \frac{4}{5}) = s i n (\frac{x}{2})$ ....(ii)
From (i), $c o s x = \frac{4}{5} \Rightarrow 1 - 2 s i n^{2} \frac{x}{2} = \frac{4}{5}$
$\Rightarrow 2 s i n^{2} \frac{x}{2} = 1 - \frac{4}{5} = \frac{1}{5} \Rightarrow s i n \frac{x}{2} = \sqrt{\frac{1}{10}}$ .

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Similar questions

s i n (\frac{1}{2} c o s^{- 1} \frac{4}{5}) =

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sin(12cos−145)=

The correct option is A 1√10Let 0≤x≤π So, cos−145=x⇒cos x=45 ....(i) Now sin(12cos−145)=sin(x2) ....(ii) From (i), cos x=45⇒1−2sin2x2=45 ⇒2sin2x2=1−45=15⇒sinx2=√110.

$s i n (\frac{1}{2} c o s^{- 1} \frac{4}{5}) =$