Question

prove that (1+Sec20+Cot70)(1-cosec20+tan70)=2

Answer 1

sec 20= 1/cos 20=1/sin 70
cot 70= cos 70/sin 70
cosec 20= 1/sin 20= 1/cos 70

(1+sec 20 + cot 70)=1+1/sin 70+ cos 70/sin 70
take lcm
(sin 70+1 + cos 70)/sin 70
similarly
(1-cosec 20+ tan 70)= (cos 70-1+ sin 70)/sin 70
multiple both

(sin70 cos70- sin 70+sin^2 70+ cos 70-1+sin70+
cos^2 70- cos 70+ sin70 cos 70)/ sin70 cos70

(2sin 70 cos 70)/ sin70 cos 70
ans=2



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