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Chapter 8 ex 8.4 questions no 1 2 |
| Answer» To convert the given trigonometric ratios in terms of cot functions, use trigonometric formulasWe know that,cosec2A\xa0– cot2A = 1cosec2A = 1\xa0+ cot2ASince cosec function is the inverse of sin function, it is written as1/sin2A = 1\xa0+ cot2ANow, rearrange the terms, it becomessin2A = 1/(1+cot2A)Now, take square roots on both sides, we getsin A = ±1/(√(1+cot2A)The above equation defines the sin function in terms of cot functionNow, to express sec function in terms of cot function, use this formulasin2A = 1/ (1+cot2A)Now, represent the sin function as cos function1 – cos2A = 1/ (1+cot2A)Rearrange the terms,cos2A = 1 – 1/(1+cot2A)⇒cos2A =\xa0(1-1+cot2A)/(1+cot2A)Since sec function is the inverse of cos function,⇒ 1/sec2A = cot2A/(1+cot2A)Take the reciprocal and square roots on both sides, we get⇒ sec A = ±√ (1+cot2A)/cotANow, to express tan function in terms of cot functiontan A = sin A/cos A and cot A = cos A/sin ASince cot function is the inverse of tan function, it is rewritten astan A = 1/cot A | |