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Please someone help I will mark him brainliest,if he do it step by step... |
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Answer» -STEP explanation:given 3 cot A = 4COT A = 4/3tan A = 3/4To prove 1 - tan^2 A / 1 + tans^2 A = cos^2 A - sin^2 ALHS = 1 - tan^2 A / 1+ tans^2 Aputting value of tan A in above equation. 1-(3/4) ^2 / 1 + (3/4) ^21-(9/16) / 1+(9/16) (7/16) / (25/16) LHS = 7/25 --------------------------- ( 1 ) now RHS is given cos^2 A - sin^2 ASO we have to cos A and sinA from tan A as they are in the RHS. using identity 1 + tan^2 A = sec^2 Aputting value of tan A 1 + 9/16 = sec^2 A25/16 = sec^2 A5/4 = secACos A = 4/5 (1/secA = cosA) also we know sin^2 A + cos^2 A = 1sin^2 A = 1 - cos^2 A putting value of cos A sin^2 A = 1 - (4/6) ^2 1 - 16/25sin^2 A = 9/25 sin A = 3/5now RHS = cos^2 A - sin^2 Aputting value of cosA and sinA RHS = (4/5) ^2 - (3/5) ^2 16/25 - 9/25RHS = 7/25 ---------------------------------( 2 ) from ( 1 ) and ( 2 ) we get LHS = RHShence (1 - tan^2 A) / (1 + tan^2 A) = cos^2A - sin^2A |
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