Reason (R): sin²A+cos²A=1
Choose the correct option:
(A)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)
(B)Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A)
(C)Assertion (A) is true but reason (R) is false.
(D)Assertion (A) is false but reason (R) is true.
CBSE Sample Question Paper 2026
Solution :
cosA+cos²A=1 (Given) —(1)
cosA=1-cos²A
cosA=sin²A — (2)
[ ∵ sin²θ+cos²θ=1]
cosA=1-cos²A
cosA=sin²A — (2)
[ ∵ sin²θ+cos²θ=1]
Now
sin²A+sin⁴A
sin²A+sin⁴A
=sin²A+(sin²A)²
=cosA+(cosA)²
=cosA+cos²A
=cosA+(cosA)²
=cosA+cos²A
=1 [From equation (1)]
Hence, sin²A+sin⁴A=1
We have proved this by using the identity sin²A+cos²A=1, which is given in assertion.
So, (A)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A), will be the correct option.