Question

sin(90-theta)cos(90-theta)=tan /1+cot²(90-theta)​

Answer 1

Step-by-step explanation:

LHS

Sin(90°-®)Cos(90°-®)

= Cos®Sin® , where ® is Theta..... (1)

RHS

Tan/1+Cot²(90°-®)

= Tan/1+Tan²®. [Cot(90°-Theta)= Tan®]

= Tan/Sec²®. [1+Tan²®=Sec²®]

= Sin/Cos÷ 1/Cos²

= Sin©Cos©....... (2)

Therefore, LHS=RHS

Answer 2

Step-by-step explanation:

LHS Sin(90_theta)cos (90 _theta)

Since sin theta. Costheta=1

RHS Tantheta/1+tan²theta

Sintheta/costheta/sec²theta

Sin²theta.1/sin²theta

1 :. LHS=RHS