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Without using trigonometry identy solve (tan 20°/cosec70°)^2+(cot20°/sec70°)+2tan15°.tan45°.tan75°​

Answer» ONG>Answer:

the SOLUTION we are going to use the followings:

SIN (90° - A) = cos A, cos (90° - B) = sin B and

{(sin C)^2} + {(cos C)^2} = 1.

(tan 20° / cosec 70°)^2 = {(tan 20°) * (sin 70°)}^2 = [(tan 20°) * {sin (90° - 20°)}]^2 = {(tan 20°) * (cos 20°)}^2 = (sin 20°)^2.

(COT 20° / sec 70°)^2 = {(cot 20°) * (cos 70°)}^2 = [(cot 20°) * {cos (90° - 20°)}]^2 = {(cot 20°) * (sin 20°)}^2 = (cos 20°)^2.

Therefore, the answer is = {(sin 20°)^2} + {(cos 20°)^2} = 1.


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