Question

show that cos+sin+tan(sin)+cot(cos)=sec+csc

Answer 1

First, we need the following simplications:

tan=sin/cos
cot=1/tan=cos/sin
sin^2+cos^2=1, and sin^2=1-cos^2, and cos^2=1-sin^2

cos+sin+(sin/cos)(sin)+(cos/sin)(cos)
=cos+sin+(sin^2/cos)+(cos^2/sin)
=cos+sin+(1-cos^2)/cos+(1-sin^2)/sin
=cos+sin+(1/cos)-(cos^2/cos)+(1/sin)-(sin^2/sin)
=cos+sin+(1/cos)-cos+(1/sin)-sin
=(1/cos)+(1/sin)=sec+csc