InterviewSolution
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InterviewSolution
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If A+B = 90°, then fill up the blanks with suitable trigonometric ratio of complementary angle of A or B.(i) sin A =…. (ii) cos B =…(iii) sec A =…(iv) tan B =…(v) cosec B =… (vi) cot A=… |
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Answer» (i) Here, A+B = 90° ⇒ A = 90° - B Multiplying both sides by Sin, we get Sin A = Sin (90° - B) ⇒ sin A = Cos B [∵ cos θ = sin (90° - θ)] (ii) Here, A+B = 90° ⇒ B = 90° - A Multiplying both sides by cos, we get Cos B = cos (90° - A) ⇒ cos B = sin A [∵ Sin θ = cos (90° - θ)] (iii) Here, A+B = 90° ⇒ A = 90° - B Multiplying both sides by sec, we get Sec A = Sec (90° - B) ⇒ sec A = Cosec B [∵ cosec θ = sec (90° - θ)] (iv) Here, A+B = 90° ⇒ B = 90° - A Multiplying both sides by tan, we get tan B = tan (90° - A) ⇒ tan B = cot A [∵ cot θ = tan (90° - θ)] (v) Here, A+B = 90° ⇒ B = 90° - A Multiplying both sides by cosec, we get Cosec B = cosec (90° - A) ⇒ cosec B = sec A [∵ sec θ = cosec (90° - θ)] (vi) Here, A+B = 90° ⇒ A = 90° - B Multiplying both sides by Sin, we get cotA = cot (90° - B) ⇒ cot A = tan B [∵ tan θ = cot (90° - θ)] |
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