Question

Solve by 'CROSS MULTIPLICATION' method

5. Find sin theta and cos theta in terms of a, b, m, n if

a sin theta + b cos theta = m ,

b sin theta - a cos theta = n


Ans:

$( \frac{am + bn}{a {}^{2} + b {}^{2} } , \frac{bm - an}{a {}^{2} + b {}^{2} } )$


Class 10

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Answer 1

tanθ=OA=Xtan⁡θ=OA=X

Therefore, O=XAO=XA

H2=O2+A2=(XA)2+A2H2=O2+A2=(XA)2+A2

=A2(1+X2)=A2(1+X2)

H=A1+X2−−−−−−√H=A1+X2

cosθ=AH=AA1+X2−−−−−−√cos⁡θ=AH=AA1+X2

cosθ=11+X2−−−−−−√cos⁡θ=11+X2

You can figure out sinθsin⁡θ using identities or

sinθ=OH=XAA1+X2−−−−−−√sin⁡θ=OH=XAA1+X2

sinθ=X1+X2−−

Answer 2

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