Question

if sin A + sin2 A =1,then find the value of cos 2 A + cos4 A

Answer 1

Answer:

→ 1 .

Step-by-step explanation :

▶ Given :-

→ sin∅ + sin²∅ = 1 .

▶ To find :-

→ cos²∅ + cos⁴∅ .

▶ Solution :-

We have,

°•° sin∅ + sin²∅ = 1 .

==> sin∅ = 1 - sin²∅ .

==> sin∅ = cos²∅ .

[ Squaring both side ] .

==> sin²∅ = cos⁴∅ .......... ( i ) .

▶ Now,

°•° cos²∅ + cos⁴∅ .

= cos²∅ + sin²∅ . [ Using ( i ) ] .

= 1 .

[ •°• sin²∅ + cos²∅ = 1 . ]

✔✔ Hence, it is founded ✅✅ .

THANKS

Answer 2

Sin A + sin^2 A = 1

Sin A = 1 - Sin ^2 A

Sin A = cos ^2 A

Sin^2 A = ( cos ^2 A ) ^2 = Cos ^4 A

Value of cos^2 A + cos ^4 A = sin A + sin^2 A

Given, sin A + sin^2 A = 1

cos^2 A + cos ^4 A = 1