Question

Verify (Prove whether true or false)
1/sec^2k=sin^2k*cos^2k+cos^4k

Answer 1

The expression is true.

Step-by-step explanation:

• Step 1: Prove the expression. 1/sec²k = sin²k cos²k + cos^4k

Left Hand Side = 1/sec²k = cos²k

Right Hand Side = sin²k cos²k + cos^4k

                            = cos²k (sin²k + cos²k)   (Taking cos²k as common)

                            = cos²k                            (∵sin²k + cos²k = 1)

⇒ Left Hand Side = Right Hand Side

So the expression is true.