Question

please answer this one

Answer 1

sec^2theta=1/cos^theta
cosec^2theta=1/sin^theta
root 0f 1/cos^theta+1/sin^theta
 root of sin^2theta+cos^2theta/sin^2theta.cos^2theta
               1 /sintheta.costheta
r.h.s=tan theta+cot theta
        =1/sintheta.costheta

Answer 2

√sec²∅ + cosec²∅ = tan∅ + cot∅
squaring on both sides.
sec²∅ + cosec²∅  = (tan∅ + cot∅)²
taking LHS
=sec²∅ + cosec²∅
=1+tan²∅ + 1 + cot²∅            (as sec²∅ = 1 + tan²∅  and cosec²∅ = 1 + cot²∅)
=tan²∅ + 2 +cot²∅
taking RHS
=(tan∅ + cot∅)²
=tan²∅ + cot²∅ + 2tan∅cot∅
=tan²∅ + cot²∅ + 2  = LHS              (as tan∅cot∅ = 1)

HENCE PROVED

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