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tanx+2tan2x+4tan4x+8cot8x=cotx

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tanx+2tan2x+4tan4x+8cot8x=cotx

    • Posted by Loveleen Jouhal 6 years, 9 months ago

    CBSE > Class 11 > Mathematics
    • 2 answers

    Aman Kumar 6 years, 9 months ago

    Wel explained answer.. thanks

    0Thank You

    Shaina Rajput 6 years, 9 months ago

    First, its important to find the value of tan x – cot x. So, tan x – cot x = tan x - 1/tan x = tan² x-1/tan x = -2 (1-tan² x/ 2tan x) = -2 ( 1/2tan x ÷ 1- tan² x) = -2× 1/tan² x = 2cot 2x ....(1) . Now— tan x + 2 tan 2x + 4 tan 4x + 8 cot 8x = tan x – cot x + 2 tan 2x + 4 tan 4x + 8 cot 8x + cot x = –2 cot 2x + 2 tan 2x + 4 tan 4x + 8 cot 8x + cot x = 2 (tan 2x – cot 2x) + 4 tan 4x + 8 cot 8x + cot x = 2 (– 2 cot 4x) + 4 tan 4x + 8 cot 8x + cot x = 4 (tan 4x – cot 4x) + 8 cot 8x + cot x = 4 (– 2 cot 8x) + 8 cot 8x + cot x = – 8 cot 8x + 8 cot 8x + cot x = cot x . Hence, tan x + 2 tan 2x + 4 tan 4x + 8 cot 8x = cot x

    2Thank You

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