Question

sinx=cosy find value x+y

Answer 1

Let a triangle ABC in one angle is 90° and y is acute
so x will be (90°-y).

now, Given
sinx+cosy=1

so,, sin(90°-x)×cosx=1

=)cosx+cosx=1.

2cosx=1

=)cosx=1/2

then cosx=cos30°

x=30°-----1)

now ,so (90°-x)=y

90°-x=y
90°-30°=y 【from 1)】

y=60°

Answer 2

Concept

The branch of mathematics that deals with measuring the sides and angles of a right-angled triangle is called Trignometry.

Sinx is defined as the ratio of the opposite side to the hypotenuse of a triangle.Cosx is defined as the ratio of the adjacent side to the hypotenuse of a triangle.

Given

The relation between Sinx and Cos in a Triangle i.e. Sinx=CosY

Find

Find the value of x+y

Solution

Let a triangle ABC in one angle is 90° and y is acute

so x will be (90°-y).

now, Given

sinx+cosy=1

so,, sin(90°-x)×cosx=1

=)cosx+cosx=1.

2cosx=1

=)cosx=1/

then cosx=cos30°

x=30°-----1)

now ,so (90°-x)=y

90°-x=y

90°-30°=y 【from 1)】

y=60°

x=30°,y=60°

Hence ,  adding the values of x and y i.e. x+y = 30°+60° =90°

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