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Express the trigonometric ratios sin A, sec A and tan A in terms of cot A.

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one month ago Anand Kumar Pandey
1372 Points
```							Dear StudentTo convert the given trigonometric ratios in terms of cot functions, use trigonometric formulas[page19image3424289280]We know that,cosec^2 A - cot^2 A = 1cosec^2 A = 1 + cot^2 ASince cosec function is the inverse of sin function, it is written as1/sin^2 A = 1 + cot^2 ANow, rearrange the terms, it becomessin^2 A = 1/(1+cot^2 A)Now, take square roots on both sides, we getsin A = ±1/(√(1+cot^2 A)The above equation defines the sin function in terms of cot functionNow, to express sec function in terms of cot function, use this formulasin^2 A = 1/(1+cot^2 A)Now, represent the sin function as cos function1 - cos^2 A = 1/(1+cot^2 A) Rearrange the terms,cos^2 A = 1 - 1/(1+cot^2 A)⇒cos^2 A = (1-1+cot^2 A)/(1+cot^2 A)Since sec function is the inverse of cos function,⇒1/sec^2 A = cot^2 A/(1+cot^2 A)Take the reciprocal and square roots on both sides, we get⇒sec A =±√(1+cot^2 A)/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 AThanks
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one month ago
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