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Question -

If cot ╬╕ = 7/8,evaluate :



Answer -


(i) (1 + sin ╬╕)(1 тАУ sin ╬╕)/(1+cos ╬╕)(1-cos ╬╕)

(ii) cot_2┬а╬╕

Solution:

Let┬аus assume a тЦ│ABC┬аin which┬атИаB = 90┬░ and тИаC = ╬╕

Given:

cot ╬╕ = BC/AB = 7/8

Let BC = 7k and AB = 8k, where k is a positivereal number

According to Pythagoras theorem in┬атЦ│ABC┬аwe get.

AC2┬а= AB2+BC2

AC2┬а= (8k)2+(7k)2

AC2┬а= 64k2+49k2

AC2┬а= 113k2

AC = тИЪ113 k

According to the sine and cos function ratios,it is written as

sin ╬╕ = AB/AC = Opposite Side/Hypotenuse =8k/тИЪ113 k = 8/тИЪ113 and

cos ╬╕ = Adjacent Side/Hypotenuse = BC/AC =7k/тИЪ113 k = 7/тИЪ113

Now apply the values of sin function and cosfunction:


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