Question

sin 50° cos 40° + sin 40° cos 50°
please explain with steps ​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

cos 50° sin 40° + sin 50° cos 40° = 1

Step-by-step explanation:

Given:

Given:(i) cos 50° sin 40° + sin 50° cos 40°

To find:

(i) The solution of the given expression.

Solution:

Solution:We know that

Solution:We know thatcos x° = sin (90°-x°)

Solution:We know thatcos x° = sin (90°-x°)So, cos 50° = sin (90°-50°) = sin 40°

Solution:We know thatcos x° = sin (90°-x°)So, cos 50° = sin (90°-50°) = sin 40°Thus,

Solution:We know thatcos x° = sin (90°-x°)So, cos 50° = sin (90°-50°) = sin 40°Thus,cos 50° sin 40° = sin 40° sin 40° = sin² 40 °

Again,

Again,sin x° = cos (90°-x°)

Again,sin x° = cos (90°-x°)So, sin 50° = cos (90°-50°) = cos 40°

Thus,

Thus,sin 50° cos 40° = cos 40° cos 40° = cos² 40 °

Therefore,

Therefore,cos 50° sin 40° + sin 50° cos 40°

Therefore,cos 50° sin 40° + sin 50° cos 40°=  sin² 40 ° + cos² 40 °

We know, sin² θ + cos² θ = 1.

We know, sin² θ + cos² θ = 1.So, sin² 40 ° + cos² 40 ° = 1.

Therefore,

Therefore,cos 50° sin 40° + sin 50° cos 40° = 1

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