Question

prove that (1-cos²A)sec²A=tan²A​

Answer 1

Prove that :-

• (1 - cos² A)sec² A = tan² A.

Answer -

LHS = RHS

Step-by-step Explanation:

Given to prove,

• (1 - cos² A)sec² A = tan² A

★ Solution :-

➝ (1 - cos² A)sec² A = tan² A

Using the trigonometric identify,

(1 - cos A) = sec A .

➝ (sin² A)sec² A = tan² A

Using the trigonometric identify,

sec A = 1/cos .

➝ (sin² A) × (1/cos² A) = tan² A

On multiplying,

➝ (sin² A × 1/cos² A) = tan² A

➝ sin² A/cos² A = tan² A

Using the trigonometric identify,

sin A/cos A = tan A .

➝ tan² A = tan² A

Therefore, LHS = RHS = tan² A.

Hence, Verified!

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Trigonometric identities used -:

• (1 - cos A) = sec A
• sec A = 1/cos
• sin A/cos A = tan A