write the formula of cos 3x in terms of tan x​

Question

write the formula of cos 3x in terms of tan x​

in progress 0
Amelia 1 month 2021-08-14T20:16:44+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-08-14T20:17:45+00:00

     Cos \: 3x \\= 4cos^{3} x - 3 cos x \\= cos x ( 4cos^{2} x - 3 ) \\= cos x [ \frac{4}{sec^{2} x } - 3 ] \\= \frac{1}{sec x } [ \frac{4}{( 1 + tan^{2} x )} - 3 ]

    /* By Trigonometric Identity */

     \boxed{ \pink { sec^{2} x = 1 + tan^{2} x }}

     = \frac{1}{\sqrt{(1+tan^{2} x )}} [ \frac{ 4 - 3(1+tan^{2} x }{(1+tan^{2} x )}] \\= \frac{1}{\sqrt{(1+tan^{2} x }} [ \frac{ 4 - 3-3tan^{2} x }{(1+tan^{2} x) }] \\= \frac{1-3tan^{2} x }{ ( 1+tan^{2}x )^{1+\frac{1}{2}} }\\= \frac{1-3tan^{2} x }{ ( 1+tan^{2}x )^{\frac{3}{2}} }

    Therefore.,

     \red{ cos 3x }\green { = \frac{1-3tan^{2} x }{ ( 1+tan^{2}x )^{\frac{3}{2}} }}

    •••♪

Leave an answer

Browse
Browse

18:9+8+9*3-7:3-1*13 = ? ( )