Question

cot (90°-)tant-cosec (90°-6)sece cos2 (50° +6) + cos2 (40°-0)
29. Simplify:
+
sin12°cos150sec78°cosec750 tan15º tan370 tan530 tan 750​

Answer 1

Answer:

Cot(90° - θ).Sin(90°-θ)/Sinθ  + Cot40°/Tan50°  - (Cos²20° + Cos²70°) = 1

Step-by-step explanation:

evaluate

cot[90-theta].sin[90-theta] / sin theta+cot 40/tan 50 - [cos square 20 +cos square 70]

Cot(90° - θ).Sin(90°-θ)/Sinθ  + Cot40°/Tan50°  - (Cos²20° + Cos²70°)

Cot(90° - θ) = Cos(90°-θ)/Sin(90°-θ)

=> Cot(90° - θ).Sin(90°-θ) = (Cos(90°-θ)/Sin(90°-θ)) * Sin(90°-θ)

=> Cot(90° - θ).Sin(90°-θ) = Cos(90°-θ)

Cot(90 - θ) = Tanθ  => Cot40° = Cot(90° - 50°)  = tan50°

Cos(90-θ) = Sinθ => Cos20° = Cos(90° - 70°) = Sin(70°)

Using all these

= Sinθ/Sinθ  +  tan50°/Tan50°  - (Sin²70° + Cos²70°)

= 1 + 1 - 1    ( using sin²θ + Cos²θ = 1)

= 1

Cot(90° - θ).Sin(90°-θ)/Sinθ  + Cot40°/Tan50°  - (Cos²20° + Cos²70°) = 1