Which of the following is the value of sin 27-cos 27-

The correct option is C none of these sin 27 ^ 0 cos 27 ^ 0 =sin 27 ^ 0 sin 63 ^ 0 #160;=2cos( 90 ^ 0 / 2 #160;) #160;sin( 36 ^ 0 / 2 ...

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Standard XII

Mathematics

Relation between Inverses of Trigonometric Functions and Their Reciprocal Functions

Which of the ...

Question

Which of the following is the value of $sin 27^{\circ} - cos 27^{\circ}$ ?

\frac{\sqrt{3 - \sqrt{5}}}{2}

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\frac{\sqrt{5 - \sqrt{5}}}{2}

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\frac{\sqrt{5} - 1}{2 \sqrt{2}}

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none of these

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Solution

The correct option is C none of these
$sin 27^{0} - cos 27^{0} = sin 27^{0} - sin 63^{0}$
$= 2 cos (\frac{90^{0}}{2}) sin (\frac{- 36^{0}}{2})$
$= - \sqrt{2} sin 18^{0} = \frac{1 - \sqrt{5}}{2 \sqrt{2}}$

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Which of the following is the value of sin27∘−cos27∘?

The correct option is C none of thesesin270−cos270=sin270−sin630=2cos(9002)sin(−3602)=−√2sin180=1−√52√2

Which of the following is the value of $sin 27^{\circ} - cos 27^{\circ}$ ?

The correct option is C none of these
$sin 27^{0} - cos 27^{0} = sin 27^{0} - sin 63^{0}$
$= 2 cos (\frac{90^{0}}{2}) sin (\frac{- 36^{0}}{2})$
$= - \sqrt{2} sin 18^{0} = \frac{1 - \sqrt{5}}{2 \sqrt{2}}$