Q. 6 C5.0( 2 Votes )

# Solve the following equations :sin x + cos x = 1

Answer :

Ideas required to solve the problem:

The general solution of any trigonometric equation is given as –

• sin x = sin y, implies x = nπ + (– 1)ny, where n Z.

• cos x = cos y, implies x = 2nπ ± y, where n Z.

• tan x = tan y, implies x = nπ + y, where n Z.

given,

.

In all such problems we try to reduce the equation in an equation involving single trigonometric expression.

{ dividing by √2 both sides}

{ }

{ cos A cos B + sin A sin B = cos (A - B)}

NOTE: We can also make the ratio of sin instead of cos , the answer remains same but the form of answer may look different, when you put values of n you will get same values with both forms

If cos x = cos y, implies x = 2nπ ± y, where n Z

s

.

.

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