Question

If sin A + sin 2A = x , cos A + c cos 2A = y then cos A =​

Answer 1

Answer:

Substituting values

[(sinA+sin2A)

2

+(cosA+cos2A)

2

][(sinA+sin2A)

2

+(cosA+cos2A)

2

−3]

=[1+1+cosA−cos3A+cos3A+cosA][2+2cosA−3]

=(2+2cosA)(2cosA−1)

=4cosA−2+4cosA−2cosA

=4cos

2

A+2cosA−2

=2(2cos

2

A−1)+2cosA

=2cos2A+2cosA

=2(cosA+cos2A)=2y

Hence proved.

Answer 2

Solution:

Substituting values

[(sinA+sin2A)

2

+(cosA+cos2A)

2

][(sinA+sin2A)

2

+(cosA+cos2A)

2

−3]

=[1+1+cosA−cos3A+cos3A+cosA][2+2cosA−3]

=(2+2cosA)(2cosA−1)

=4cosA−2+4cosA−2cosA

=4cos

2

A+2cosA−2

=2(2cos

2

A−1)+2cosA

=2cos2A+2cosA

=2(cosA+cos2A)=2y

Hence proved.

Was this answer helpful?