If sin(50-3/2x) = cos(3x-50) then find x. and hence evaluate tanx.secx.sinx-cotx.sinx.cosx.

Asked by neeraj | 29th Sep, 2015, 02:41: PM

Expert Answer:

G i v e n space t h a t comma space sin open parentheses 50 degree minus fraction numerator 3 x over denominator 2 end fraction close parentheses equals cos open parentheses 3 x minus 50 degree close parentheses rightwards double arrow s i n open parentheses 50 degree minus fraction numerator 3 x over denominator 2 end fraction close parentheses equals sin open square brackets 90 degree minus open parentheses 3 x minus 50 degree close parentheses close square brackets rightwards double arrow s i n open parentheses 50 degree minus fraction numerator 3 x over denominator 2 end fraction close parentheses equals s i n open square brackets 90 degree minus 3 x plus 50 degree close square brackets rightwards double arrow s i n open parentheses 50 degree minus fraction numerator 3 x over denominator 2 end fraction close parentheses equals s i n open square brackets 140 degree minus 3 x close square brackets rightwards double arrow 50 degree minus fraction numerator 3 x over denominator 2 end fraction equals 140 degree minus 3 x rightwards double arrow 3 x minus fraction numerator 3 x over denominator 2 end fraction equals 140 degree minus 50 degree rightwards double arrow 3 x minus fraction numerator 3 x over denominator 2 end fraction equals 90 degree rightwards double arrow 3 x open parentheses 1 minus 1 half close parentheses equals 90 degree rightwards double arrow fraction numerator 3 x over denominator 2 end fraction equals 90 degree rightwards double arrow x over 2 equals 30 degree rightwards double arrow x equals 60 degree W e space n e e d space t o space e v a l u a t e comma space tan x cross times s e c x cross times sin x minus c o t x cross times sin x cross times cos x. T h u s comma space space t a n x cross times s e c x cross times s i n x minus c o t x cross times s i n x cross times c o s x equals space t a n 60 degree cross times s e c 60 degree cross times s i n 60 degree minus c o t 60 degree cross times s i n 60 degree cross times c o s 60 degree equals square root of 3 cross times 2 cross times fraction numerator square root of 3 over denominator 2 end fraction minus fraction numerator 1 over denominator square root of 3 end fraction cross times fraction numerator square root of 3 over denominator 2 end fraction cross times 1 half equals 3 minus 1 fourth equals 11 over 4

Answered by Vimala Ramamurthy | 30th Sep, 2015, 08:50: AM