Question

What is the value of cos 50 sin 40 + sin 50 cos 40

Answer 1

sin(90-50) sin 40 + cos (90-50) cos 40
sin40 sin40 + cos40 cos40
sin^2 40 + cos^2 40
(since sin @ + cos@ =1)
so sin^2 40 + cos^2 40 = 1

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Answer 2

Given:

(i) cos 50° sin 40° + sin 50° cos 40°

To find:

(i) The solution of the given expression.

Solution:

We know that

cos x° = sin (90°-x°)

So, cos 50° = sin (90°-50°) = sin 40°

Thus,

cos 50° sin 40° = sin 40° sin 40° = sin² 40 °

Again,

sin x° = cos (90°-x°)

So, sin 50° = cos (90°-50°) = cos 40°

Thus,

sin 50° cos 40° = cos 40° cos 40° = cos² 40 °

Therefore,

cos 50° sin 40° + sin 50° cos 40°

=  sin² 40 ° + cos² 40 °

We know, sin² θ + cos² θ = 1.

So, sin² 40 ° + cos² 40 ° = 1.

Therefore,

cos 50° sin 40° + sin 50° cos 40° = 1