Question

if cos A+cos2 A=1, find the value of sin2 A+ sin4 A​

Answer 1

Cos A+Cos2A=1

=> cosA = 1 – cos2A = sin2A

So, Required is

sin2A + sin4A

= Cos A+Cos2A

=1

Since cos A + cos2 A=1

Now,cosA= 1-cos2A=sin2A

Then taking L.H.S. sin2A+sin4A

=Sin2A(1+sin2A)

=CosA(1+cosA)

CosA+cos2A=1(given)

L.H.S =1 Hence proved

Cosa+cos^2=1

Cosa+1-sin2a=1

Cosa-sin2a=0

Cosa=sin2a

Squaring both side

Cos2a=sin4a

Sin2a+sin4a=1

Sin2a+cos2a=1

1=1

CosA+cos^2=1

CosA+1-Sin^2A=1

CosA-Sin^2A=0

CosA=Sin^2A

Sq both side

Cos^2A=Sin^4A

1-Sin^2A=Sin^4A

1=Sin^4A+Sin^2A

Hence ,

Ans is 1....

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