Math, asked by karajrandhawa3943, 1 year ago

Formula of sin square A - sin square B

Answers

Answered by Anonymous
13

Answer:

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Step-by-step explanation:

sin^2A+sin^2B=? sin^2A+sin^2B=1-cos(A+B).

Answered by rinayjainsl
0

Answer:

The formula for given expression is

 \sin {}^{2}A -  \sin {}^{2} B  \\ =  \sin(A + B)  \sin(A  -  B)

Step-by-step explanation:

Given expression is

sin^2{A}-Sin^2{B}

Using the relation of algebra,

a {}^{2}  - b {}^{2}  = (a + b)(a - b)

We write the given expression as

sin {}^{2} A - sin {}^{2} B  \\ = (sinA  + sinB)(sinA - sinB)

We have some trigonometric relations which are written below

sin \alpha  + sin \beta  \\  = 2sin( \frac{ \alpha  +  \beta }{2} )cos( \frac{ \alpha  -  \beta }{2} ) \\  \\ sin \alpha   - sin \beta  \\  = 2cos( \frac{ \alpha  +  \beta }{2} )sin( \frac{ \alpha  -  \beta }{2} )

Based on this relations our expression is transformed as

sin {A}^{2}  - sin {B}^{2}   \\ = 2sin( \frac{A + B}{2} )cos( \frac{A - B}{2} ) \times 2cos( \frac{A + B}{2} )sin( \frac{A - B}{2} ) \\  = (2sin( \frac{A + B}{2} )cos( \frac{A + B}{2} ))(2sin( \frac{A  -  B}{2})(cos( \frac{A + B}{2} ))

For a fact,we know that

2sin \alpha cos \alpha  = sin2 \alpha

Hence,the expression becomes

 \sin {}^{2}A -  \sin {}^{2} B  \\ =  \sin(A + B)  \sin(A  -  B)

Therefore,the formula of the given expression is obtained using algebraic and trigonometric identities.

#SPJ3

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