Question

Q. Prove that -- sin square theta * cos square theta + tan theta * sin theta + cos cube theta = sec theta ​

Answer 1

To Prove :

sin²θ.cosθ + tanθ.sinθ + cos³θ = secθ

Proof :

L.H.S

=> sin²θ.cosθ + tanθ.sinθ + cos³θ

=> (sin²θ.cosθ + cos³θ) + tanθ.sinθ

=> cosθ (sin²θ + cos²θ) + tanθ.sinθ

=> cosθ (1) + tanθ.sinθ

=> cosθ + sinθ/cosθ × sinθ

=> cosθ + (sin²θ/cosθ)

=> (cos²θ + sin²θ)/cosθ

=> 1/cosθ

=> secθ

R.H.S

∴ Hence, proved !