Question

Cos9°+sin9°=√2sin54°

Answer 1

Answer:

Step-by-step explanation:

Cos9°+sin9°=√sin45°

L.H.S

1.cos9°+1.sin9°

=√2.(1/√2.cos9°+1/√2.sin9°)

=√2(sin45°cos9°+cos45°sin9°)

=√2sin(45°+9°)

=√2sin54°

Answer 2

Hence proved that Cos9° + sin9° = √2sin54°

Step-by-step explanation:

Given,

Cos9° + sin9° = √2sin54°

To solve,

R.H.S.

= $\sqrt{2}$ Sin (45° + 9°)

= $\sqrt{2}$ (Sin 45° Cos9° + Cos45° Sin 9°)

= $\sqrt{2}$ * (1/$\sqrt{2}$) Cos9° + $\sqrt{2}$ * (1/$\sqrt{2}$) Sin 9°

By cancelling both $\sqrt{2}$ with $\sqrt{2}$, we get;

= Cos9° + Sin9°

= L.H.S.

Hence proved L.H.S. = R.H.S.

Learn more: Trigonometry

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