Q. 45.0( 2 Votes )

If A+B=90o, 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=…

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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