Question

Cos100°cos40°+sin100°sin40°=1/2

Answer 1

Answer:

1/2

Step-by-step explanation:

1/2

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Answer 2

Concept

Angle measurement and angle-related issues are covered in basic trigonometry. Sine, cosine, and tangent are the three fundamental operations of trigonometry. Other significant trigonometric functions, such as cotangent, secant, and cosec. In trigonometry, there are six fundamental ratios that are used to establish a connection between a right triangle's side-to-angle ratio and its angle.

Given

cos100°cos40° ₊ sin100°sin40° = 1/2

Find

we need to prove the above expression,

Solution

given, cos100°cos40° ₊ sin100°sin40° = 1/2

L.H.S = cos100°cos40° ₊ sin100°sin40°

cos100°cos40°+sin100°sin40°

This is in the form of cosAcosB+sinAsinB=cos(A−B)

Therefore, cos100°cos40°+sin100° sin40° = cos(100° −40°)

⇒cos100°cos40° +sin100°sin40°=cos60°

⇒cos100° cos40°+sin100°sin40°= 1/2

therefore L.H.S = R.H.S

hence proved.

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