Question

6. Find the value of sin 75° sin 15°.​

Answer 1

Answer:

sin75'sin15'=sin(90'-15')sin15'

=cos15'sin15'

=1/2multiple2sin15'cos15'

=1/2sin2multiple15'

=1/2sin30'

=1/2mult1/2

=1/4

Answer 2

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Your Answer is Below

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Question :-

sin 75° sin 15°

Explanation :-

sin 75° sin 15°

$\mathrm{Use\:the\:following\:identity}:\quad \sin \left(s\right)\sin \left(t\right)=\frac{-\cos \left(s+t\right)+\cos \left(s-t\right)}{2}$

⇒ $\sin \left(75^{\circ \:}\right)\sin \left(15^{\circ \:}\right)=\frac{-\cos \left(75^{\circ \:}+15^{\circ \:}\right)+\cos \left(75^{\circ \:}-15^{\circ \:}\right)}{2}$

⇒ $\frac{-\cos \left(90^{\circ \:}\right)+\cos \left(60^{\circ \:}\right)}{2}$

⇒ $\frac{-\cos \left(90^{\circ \:}\right)+\cos \left(60^{\circ \:}\right)}{2}$

• Cos ( 90° ) = 0
• Cos ( 60° ) = $\huge\frac{1}{2}$

⇒ $\frac{-0\ +\ \frac{1}{2}}{2}$

⇒ $\frac{1}{2\ \cdot \ 2 }$

⇒ $\frac{1}{4}$

                          $\huge{\orange{\boxed{\boxed{\pink{\underline{\green{\mathscr{ \sin \left(75^{\circ \:}\right)\sin \left(15^{\circ \:}\right) = \frac{1}{4} }}} }} }}}$

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Hope It Helps You Dear ! :D  ^_^

By Abhiram5566

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