Question

Tan/1-cot + cot /1-tan = 1+sec .cosec

Answer 1

Answer:

refer to the attached. .......

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Answer 2

Step-by-step explanation:

as per the question,

tan/1-cot+cot/1-tan=1+sec.cosec

turn all in terms of sin,in LHS

sin/cos/1-cos/sin+cos/sin/1-sin/cos

sin/cos/sin-cos/sin+cos/sin/cos-sin/cos

sin/cos×sin/sin-cos+cos/sin×cos/cos-sin

sin square/cos(sin-cos) +cos square /sin(cos-sin)

sin square /cos(sin-cos)-cos square /sin(sin-cos)

take sin-cos as common

1/sin-cos×{sin square/cos-cos square/sin}

1/sin-cos×{sin cube-cos cube/sincos}

1/sin-cos×{sin square+cos square +(sin -cos) }[by using identity ]

now by simplifying the terms we gets

1+1/sincos

1+1/sin.1/cos

1+sec.cosec

therefore hence LHS=RHS