Question

find the value of sin 90 sin 60 + Cos 60 cos 90​

Answer 1

Answer:

√3/2

Step-by-step explanation:

sin 90° sin 60° + Cos 60° cos 90°

1 × √3/2 + 1/2× 0

√3/2 + 0

√3/2

Answer 2

The value of sin90sin60 + cos60cos90 is √3/2.

Given:

The expression sin90sin60 + cos60cos90​.

To Find:

The value of the given expression.

Solution:

Let us find the value of the individual terms.

sin 90 = 1

sin 60 = √3/2

cos 60 = 1/2

cos 90 = 0.

⇒ sin90sin60 + cos60cos90 = 1x(√3/2) + (1/2)x0 = √3/2.

We can also solve the given question using the below identity for trigonometric ratios involving two different angles A and B:

cos (A - B) = cosAcosB + sinAsinB.

We are given the expression:

sin90sin60 + cos60cos90 = cos90cos60 + sin90sin60

= cos (90-60)

= cos (30) = √3/2

∴ The value of sin90sin60 + cos60cos90 is √3/2.

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