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CBSE Class 11-science Answered

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 | 30 Jul, 2019, 11:19: AM
answered-by-expert 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 | 31 Jul, 2019, 10:20: AM

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