Find the values of x for which it satisfies tanx = cot 5 x as well as sin 2x = cos 4x [x€ (-π/2,π/2)]

Asked by sajal2402 | 30th Jul, 2019, 11:19: AM

Expert Answer:

tan x = cot 5x
tan x = tan (90-5x)
x equals n straight pi plus straight pi over 2 minus 5 straight x
straight x equals nπ over 6 plus straight pi over 12
straight x equals plus-or-minus straight pi over 12 comma plus-or-minus straight pi over 4 comma plus-or-minus fraction numerator 5 straight pi over denominator 12 end fraction
Also comma space sin space 2 straight x equals cos space 4 straight x
sin space 2 straight x equals 1 minus 2 sin squared 2 straight x
rightwards double arrow 2 sin squared 2 straight x plus sin space 2 straight x minus 1 equals 0
rightwards double arrow sin space 2 straight x equals negative 1 space or space sin space 2 straight x equals 1 half
rightwards double arrow 2 straight x equals negative straight pi over 2 space or space 2 straight x equals straight pi over 6 or fraction numerator 5 straight pi over denominator 6 end fraction
rightwards double arrow straight x equals negative straight pi over 4 comma straight pi over 12 comma fraction numerator 5 straight pi over denominator 12 end fraction
Hence comma space the space values space of space straight x space are space minus straight pi over 4 comma straight pi over 12 comma fraction numerator 5 straight pi over denominator 12 end fraction.

Answered by Renu Varma | 31st Jul, 2019, 10:20: AM