Write ‘True’ or ‘False’ and justify your answer.If cosA + cos2

1.	Write ‘True’ or ‘False’ and justify your answer.If cosA + cos2A = 1, then sin2A + sin4A = 1.
Answer» True Justification: According to the question, cos A+cos² A = 1 i.e., cos A = 1- cos² A Since, sin² θ+cos² θ = 1 sin² θ = 1- cos² θ) We get, cos A = sin² A …(1) Squaring L.H.S and R.H.S, cos² A = sin⁴ A …(2) To find sin²A+sin⁴ A=1 Adding equations (1) and (2), We get sin²A + sin⁴ A= cos A + cos² A Therefore, sin²A + sin⁴ A = 1

Write ‘True’ or ‘False’ and justify your answer.If cosA + cos2A = 1, then sin2A + sin4A = 1.

Answer»

True

Justification:

According to the question,

cos A+cos² A = 1

i.e., cos A = 1- cos² A

Since,

sin² θ+cos² θ = 1

sin² θ = 1- cos² θ)

We get,

cos A = sin² A …(1)

Squaring L.H.S and R.H.S,

cos² A = sin⁴ A …(2)

To find sin²A+sin⁴ A=1

Adding equations (1) and (2),

We get

sin²A + sin⁴ A= cos A + cos² A

Therefore, sin²A + sin⁴ A = 1