Question

If sin A + tan A = p ; then prove that cosec A = (In attachment)
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Answer 1

Answer:

Step-by-step explanation:

secA+tanA=p .....(i)

We know sec2A–tan2A=1

=>(secA–tanA)(secA+tanA)=1

=>(secA–tanA)(p)=1

=>secA–tanA=1p .....(ii)

Adding (i) and (ii)

secA+tanA+secA–tanA=p+1p

=>2secA=p2+1p

=>secA=p2+12p

=>cosA=2pp2+1

=>1–sin2A−−−−−−−√=2pp2+1

=>sin2A=1−(2pp2+1)2

=>sin2A=1−(4p2(p2+1)2)

=>sin2A=((p2+1)2−4p2(p2+1)2)

=>sin2A=((p2−1)2(p2+1)2)

=>sin2A=(p2−1p2+1)2

=>sinA=p2−1p2+1

=>cosecA=p2+1p2−1