Question

1/ ( tan A + cot A ) = cos A sin A

Answer 1

Taken the L.H.S is 1/ ( tan A + cot A )

= 1/1/ (sin²A + cos²A) / sinA cosA

=1/1/1/sinA cosA

= sinA cosA

identity used here :-

sin²A + cos²A = 1

tanA = sinA / cosA

cotA = cosA / sinA

Answer 2

Answer:

L.H.S=1/(tan A+cot A)

=(sin 2A +cos2A) / (tanA+cotA)

[since ,,,,,sin2A+cos2A=1]

=(sin2A+cos2A)/(sinA/cosA)+(cosA/sinA)

[since,,,,, tan=(sin/cos) and cot =(cos/sin)]

=(sin2A+cos2A)/[(sin2A+cos2A)/sin.cos]

=[(sin2A+cos2A).(sinA*cosA)]/sin2A+cos2A

=[1.(sin*cos)]/1

[since,,,,, sin2A. cos2A=1]

=sin A*cosA=R.H.S

plz ,,,,,,,,,note that the dot(.) between the sin and cos indicates multiplication,,,,,,,,,