Question

sin 65+cos 65=√2 cos 20
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Answer 1

Answer:

Hi

Explanation:

To prove:sin65+cos65=$cos20\sqrt{x}$

Proof:

L.H.S

sin65+cos65

sin65+cos(90-65)[∴complementary angle]

sin65+sin25

2sin(65+25)/2 cos(65-25) [∴sinA+sinA 2sin(A+B)/2 cos(A-B)/2]

2sin45 cos20

2×$1/\sqrt 2$ cos20 [∴sin45=$1/\sqrt{ 2$]

$\sqrt2$cos20

=R.H.S

∴Hence proved.

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