Question

Prove that Sin A = Cos ( 90- A) and Tan A = cot (90 - A)

Answer 1

Answer:

since, angle A + angle C = 90°, they form such a pair we have,

sin A = BC/AC}--------(1)

cos A = AB/AC }-------(1)

tan A = BC/AB }-------(1)

cot A = AB/BC }-------(1)

you will observe that angle C= (90° - angleA)

Now, Let us write the trigonometric ratios for angle C = (90° - angle A)

sin (90° - A) = AB/AC }--------(2)

cos (90° - A) = BC/AC }-------(2)

tan (90° - A) = AB/BC }--------(2)

cot (90° - A) = BC/AB }---------(2)

Now, compare the ratios in (1) and (2) and observe that, sin A = cos (90° - A)

tan A = cot (90° - A) proved

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