If 3 cot A = 4, check whether (1-tan^2 A)/(1+tan^2 A) = cos^2A - sin^2 A or not.

Given, ⇒ 3 cot A = 4 ⇒ cot A = Let us draw a right angle triangle ABC. We know that, cot A = Substituting values, we get : Let AB = 4k and BC = 3k. In right angle triangle ABC, ⇒ AC 2 = AB 2 + BC 2 ⇒ AC 2 = (4k) 2 + (3k) 2 ⇒ AC 2 = 16k 2 + 9k 2 ⇒ AC 2 = 25k 2 ⇒ AC = = 5k. We know that, tan A = . Substituting value of tan A in We know that, cos A = . sin A = . Substituting value of cos A and sin A in cos 2 A - sin 2 A, we get : Hence, proved that = cos 2 A - sin 2 A.

If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠A = ∠B.

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In △ PQR, right-angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of sin P, cos P and tan P.

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Mathematics

If 3 cot A = 4, check whether (1-tan^2 A)/(1+tan^2 A) = cos^2A - sin^2 A or not.

Trigonometric Identities

Related Questions

If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠A = ∠B.

In △ PQR, right-angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of sin P, cos P and tan P.