Home
Class 12
MATHS
If tan((alphapi)/(4))=cot((betapi)/(4)),...

If `tan((alphapi)/(4))=cot((betapi)/(4)),` then

A

`alpha+beta=0`

B

`alpha+beta=2n`

C

`alpha+beta=2n+1`

D

`alpha+beta=2(2n+1),AAninI`

Text Solution

Verified by Experts

The correct Answer is:
D
Given , `tan((alphapi)/(4))=tan((pi)/(2)-(beta)/(4))`
`(alphapi)/(4)=npi+(pi)/(2)-(betapi)/(4)`
`rArr(alpha+beta)(pi)/(4)=((2n+1)/(2))pi`
`rArralpha+beta=2(2n+1),AA ninI`
Promotional Banner

Similar Questions

Explore conceptually related problems

(sec2x-tan2x) equals a tan(x-(pi)/(4))b)tan((pi)/(4)-x)c cot(x-(pi)/(4))d tan^(2)(x+(pi)/(4))

If y=(sqrt(1-sin4A)+1)/(sqrt(1+sin4A)-1) then one if the values of y is (A)-tan A(B)cot A(C)tan((pi)/(4)+A)(D)-cot((pi)/(4)+A)

If: cos(tan^(-1)x)=sin (cot^(-1).(3)/(4)), then : x =

Find the value tan((pi)/(5))+2tan((2 pi)/(5))+4cot((4 pi)/(5))

If tan^(-1)x+tan^(-1)y=(pi)/(4) , then cot^(-1)x+cot^(-1)y=

If tan 4 theta = cot (2 theta +30^(@)) , then theta is equal to :

If tan x=a, then cot(x-(pi)/(4)) equals

If tan^(-1) x + tan^(-1) y = (4pi)/(5) , then cot^(-1) x + cot^(-1) y equal to

Let theta in(0,(pi)/(4)) and t_(1)=(tan theta)^(tan theta),t_(2)=(tan theta)6(cot theta),t_(3)=(cot theta)^(tan theta) and t_(4)=(cot theta)^(cot theta) then

prove that :tan^(-1)(((1)/(2))tan2A)+tan^(-1)(cot A)+tan^(-1)(cot^(3)A)={0when(pi)/(4)