Question

The value of Sin (45+thetta) - cos(45-thetta) is equal to _______
A) 2 COS THETTA
B) 0
C) 2 SIN THETTA
D) 1

Answer 1

Option B i.e, 0 is the correct answer.

Step-by-step explanation:

Given that:  $Sin(45+\theta)-Cos(45-\theta)$

Formula:

$Sin(A + B) = SinA.CosB + CosA.SinB \\ \\Cos(A-B)=CosACosB+SinASinB$

Equation:

$Sin(45+\theta)-Cos(45-\theta)$

Solve equation by applying above formula:

$(Sin45.Cos\theta+Cos45.Sin\theta)-(Cos45.Cos\theta+Sin45.Sin\theta)$

$Sin 45^{\circ}=\frac{1}{\sqrt{2}}\ \ and \ \ Cos 45^{\circ}= \frac{1}{\sqrt{2}}$

$(\frac{1}{\sqrt{2} }.Cos\theta+\frac{1}{\sqrt{2}}.Sin\theta) -(\frac{1}{\sqrt{2}}.Cos\theta+ \frac{1}{\sqrt{2}}.Sin\theta)$

$\frac{1}{\sqrt{2} }.Cos\theta+\frac{1}{\sqrt{2}}.Sin\theta$$-\frac{1}{\sqrt{2}}.Cos\theta-\frac{1}{\sqrt{2}}.Sin\theta$

= 0.

That's why the  option B is correct.

Learn more:

• Formula: https://brainly.in/question/5969501