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Prove that(cos theta – sintheta+1)/(costheta + sintheta+1)= cosectheta + cottheta |
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Answer» Answer :- solving LHS, → (cosA - SINA + 1)/(cos A + sinA - 1) dividing numerator and denominator by sinA → (cosA / sinA - sinA/sinA + 1/sinA) / (cosA / sinA + sinA/sinA - 1/sinA) → (cot A + COSEC A - 1) / (cot A - cosec A + 1) putting 1 = cosec²A - cot²A in numerator, → {cot A + cosec A - (cosec²A - cot²A)} / (cot A - cosec A + 1) → using (a² - b²) = (a + b)(a - b) → (cotA + cosecA)(1 - cosecA + cotA) / (cot A - cosec A + 1) → cotA + cosecA = RHS (PROVED) Learn more :- It SINO + tano = m tano - sino an Then express the values of m²-n² in terms of M and N tanA/(1-cotA) + cotA/(1-tanA) |
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