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पंकज कुमार

· started a discussion

· 1 Months ago

11 (Question:614840.0)

solution is not currect

Question:

2 tan–1 {cosec (tan–1 x) – tan (cot–1 x)} is equal to:

Options:
A)

cot–1 x

B)

cot–1  1x   

C)

tan–1 x

D)

None of these

Solution:

Ans:(c) 

2 tan-1{cos\(\mu\) (tan-1x) - tan (cot-1x)}

= 2 tan-1{cos\(\mu\) (cos\(\mu\) \(\cfrac{\sqrt{1+x^2}}{x}\) - tan/tan/1/x)}

= 2 tan-1(\(\cfrac{\sqrt{1+x^2}-1}{x}\)   )

put x = tan \(\theta\)

= 2 tan-1 (\(\cfrac{\sqrt{1+tan^2ϑ} \ -1}{x}\)  )

= 2 tan-1 (\(\cfrac{secϑ-1}{tanϑ}\))

= 2 tan-1 (\(\cfrac{1-cosϑ}{sinϑ}\))

= 2 tan-1 {\(\cfrac{2 sin^2 \cfrac{ϑ}{2}}{2 sin \cfrac{ϑ}{2}cos\cfrac{ϑ}{2}}\)}

= 2 tan-1 \(\cfrac{ϑ}{2}\) 

= ϑ = tan-1 x

Knowledge Expert

· commented

· 1 Months ago

Dear student,
Given solution is correct.
Keep learning,
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