Prove that tanx + cotx=2cosec2x and deduce that tan75 + cot75=4.
Answers
Answered by
78
tan x + cot x = sinx /cos x + cos x /sin x
=( sin²x + cos²x) /sinx cos x
= 2 / 2sinx cos x
= 2/sin 2x
= 2 cosec 2x
tan 75 + cot 75 =2 cosec 150 = 2 × 2 = 4
=( sin²x + cos²x) /sinx cos x
= 2 / 2sinx cos x
= 2/sin 2x
= 2 cosec 2x
tan 75 + cot 75 =2 cosec 150 = 2 × 2 = 4
Answered by
21
Answer:
Step-by-step explanation:
LHS = tan(x) + 1/tan(x) = { [tan(x)]^2 + 1}/tan(x)
= [sec(x)]^2 /tan(x) = 1 /sin(x)cos(x) = 2 /sin(2x) = 2*cosec(2x) = RHS
tan(75) + cot(75) = 2*cosec(150) = 2 /sin(150) = 2 /sin(30) = 4
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