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If 5[tan^2x-cos^2x]=2cos2x+9 then find the value of cos4x a).1/3 b). 2/9 c).-7/9 d).-3/5

If 5[tan^2x-cos^2x]=2cos2x+9 then find the value of cos4x
a).1/3 b). 2/9 c).-7/9 d).-3/5

Grade:11

2 Answers

Ayanava Datta
40 Points
3 years ago
5(tan2x-cos2x)=2cos2x+9
(5/a2)-5a2-14=2(2a2-1)    [a=cosx]
5-9a4-12a2=0
9a4+12a2-5=0
(3a2+5)(3a2-1)=0
a2​=(-5/3)/(1/3)
a squre can’t be -ve
a2=(1/3)
cos2x=(1/3)
cos4x=2(2cos2x-1)2-1
         =(-7/9)
ans: (c)
ankit singh
askIITians Faculty 614 Points
10 months ago
If 5(tan^2 x – cos^2x) = 2 cos 2x + 9, then the value of cos 4x is ... -3/5; 1/3; 2/9; -7/9 ... 5(sec2 x – 1 – cos2 x) = 2(2cos2 x – 1) + 9 ... -7/9.      
thank u regards ankit singh manit bhopal
 

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