Question

If sin2A+sinA=1
Prove cos2A+cos4A=1

Answer 1

We have,

sinA + sin²A = 1   ...(1) 

⇒ sinA = 1 – sin²A   ...(2)

Now

cos²A + $cos^{4} A$ 

= (1 – sin²A) + {(1 – sin²A)}²

= sinA + sin²A [from (2)]  

= 1 [from (1)]

Hope It Helps :)

Answer 2

sin^2A + sin A = 1 -------(2)

we know that,
sin^2 A + cos^2 A = 1 -------(1)

By comparing equation (1) & (2) we get to know ;

sinA = cos^2 A ---------(3)

squaring both sides ;
sin^2 A = cos^4 A ------(4)

==========================
Now ,
L.H.S
= cos^2 A + cos^4 A

Put the values from equation (3) & (4)

= sin A + sin^2 A

= equation (1)
= 1
= R.H.S
---------------- Hence Proved
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