Question

(sin theta+ cos theta)(sec theta + cosec theta)=2+sec theta cosec theta

Answer 1

Let us assume theta as -@ symbol for a while
Now( sin@+cos@)(sec@+cosec@)
=(sin@+cos@)(1/cos@+1/sin@)
=(sin@+cos@)(sin@+cos@/sin@cos@)
=square of (sin@+cos@)/sin@cos@
=square of sin@+square of cos@+2cos@sin@/sin@cos@
=1+2sin@cos@/sin@cos@
=sec@cosec@+2

Now putting theta we get,
sin theta+cos theta=2+sec theta cosec theta
L:H:S=R:H:S: proved