Question

Prove (cosec A-sinA)(sec A-cos A)sec^2A=tanA

Answer 1

Answer:

put A=45° question will be itself proved

Answer 2

Step-by-step explanation:

L.H.S :-

(Cosec A - Sin A) (Sec A - Cos A) Sec²A

∵

• Cosec A = 1/Sin A
• Sec A = 1/Cos A
• Sec²A = 1/Cos²A

∴

(1/Sin A - Sin A) (1/Cos A - Cos A) (1/Cos²A)

L.C.M :-

(1 - Sin²A)/Sin A (1 - Cos²A)/Cos A (1/Cos²A)

Cos²A/Sin A × Sin²A/Cos A × 1/Cos²A

Cancellation of numerator and denominator.

Sin A/Cos A

∵ Sin A/Cos A = Tan A

∴ L.H.S = R.H.S