Question

Find the possible value of cosx, If cot x + cosecx = 5​

Answer 1

Answer:

Find the possible value of cos x , if cot x +cosec x= 5.

Easy

cotx+cosecx=5sinxcosx+sinx1=5cosx+1=5sinx

squaring both sides

(cosx+1)2=(5sinx)2cos2x+1+2cosx=25sin2xcos2x+1+2cosx=25(1−cos2x)26cos2x+2cosx−24=0

dividing by 2 we get

13cos2x+13cosx−12cosx−12=013cosx(cosx+1)−12(cosx+1)=0(13cosx−12)(cosx+1)cosx=1312orcosx=−1

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Answer 2

Step-by-step explanation:

cotx+cosecx=5

sinxcosx + sinx1=5

cosx+1=5sinx

squaring both sides

(cosx+1) 2=(5sinx) 2cos 2x+1+2cosx

=25sin 2 xcos 2

x+1+2cosx=25(1−cos 2x)26cos 2

x+2cosx−24=0

dividing by 2 we get

13cos 2 x+13cosx−12cosx−12=0

13cosx(cosx+1)−12(cosx+1)=0

(13cosx−12)(cosx+1)

cosx= 1312

or

cosx=−1