Question

2cos22 1/2cos67 1/2 evaluate

Answer 1

Answer:

$\red {Value \: of \: 2cos22\frac{1}{2} cos67\frac{1}{2}} \green {= \frac{1}{\sqrt{2}}}$

Step-by-step explanation:

$Value \: of \: 2cos22\frac{1}{2} cos67\frac{1}{2}\\= 2cos22\frac{1}{2} cos (90-22\frac{1}{2})\\= 2cos22\frac{1}{2} sin 22\frac{1}{2}$

$\boxed { \pink { cos (90- \theta) = sin\theta }}$

$= sin 2\times 22\frac{1}{2}$

$\boxed { \orange { 2sinAcosA = sin2A }}$

$= sin 45\degree$

$= \frac{1}{\sqrt{2}}$

Therefore.,

$\red {Value \: of \: 2cos22\frac{1}{2} cos67\frac{1}{2}} \green {= \frac{1}{\sqrt{2}}}$

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