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If 3 cot A = 4, check whether1 - tan" A1 + tan-A= cos A-sin A or not. |
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Answer» Given 3 COTA = 4. cotA = 4/3. ----------------- (1).We KNOW that tan theta = 1/cot theta tan A = 1/cotA = 1/4/3 = 3/4. --------------- (2)We know that COSEC^2 theta = 1 + cot^2 theta = 1 + (4/3)^2 = 1 + 16/9 = 25/9. cosec theta = 5/3. ---------------- (3)We know that cosec theta = 1/sin theta (5/3) = 1/sin theta 5sin theta = 3 sin theta = 3/5 ------------- (4)We know that cos^2 theta = 1 - sin^2 theta = 1 - (3/5)^2 = 1 - 9/25 = 25 - 9/25 = 16/25 cos A = 4/5. ------------- (5)Now, LHS:\frac{1 - tan^2A}{1 + tan^2A} 1+tan 2 A1−tan 2 A \frac{1 - (\frac{3}{4})^2 }{1 + ( \frac{3}{4})^2 } 1+( 43 ) 2 1−( 43 ) 2 \frac{1 - \frac{9}{16} }{1 + \frac{9}{16} } 1+ 169 1− 169 \frac{16 - 9}{16 + 9} 16+916−9 \frac{7}{25} 257 .Now, RHS: (4)&(5)cos^2A - sin^2Acos 2 A−sin 2 A( \frac{4}{5})^2 - ( \frac{3}{5} )^2( 54 ) 2 −( 53 ) 2 \frac{16}{25} - \frac{9}{25} 2516 − 259 \frac{16-9}{25} 2516−9 \frac{7}{25} 257 LHS = RHS |
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