Question

If sin theta + cos theta = √2 ,then evaluate : tan theta + cot theta

Answer 1

squaring first equatio
sin^2(a)+cos^2(a) +2sin( a) cos( a)=2
1+2sin(a)cos(a)=2
2sin(a)cos(a)=1
sin(a)cos(a)=1/2
tan a+cot a=sin a/cos a +cos a/sin a
=sin ^2 a +cos ^2 a/sin a cos a
=1/(1/2)
=2

Answer 2

Answer:

2

Step-by-step explanation:

First, lets square the given equation to remove the root.

[sina +cosa]^2 =2

sin^2A + cos^2A + 2sinAcosA =2

1 +2sinAcosA=2                                  [sin^2A+cos^2A=1]

2sinAcosA=2-1

sinAcosA=1/2              [eqn.1]

leave the given result here.Proceed with the other one

tanA+ cotA=sinA/cosA + cosA/sinA

next take the LCM

sin^2A +co^2A/sinAcosA     [ eqn.2]

substitute eqn 1 in eqn 2

1/1/2=2

hence the value of tanA+cotA= 2