Answers

  • Brainly User
2014-04-01T18:37:19+05:30
A)
 a^{2}-b^2=(a-b)(a+b) formula used
(sin^2x+cos^2x)=1
cos^4 x - sin^4 x=(sin^2x+cos^2x)(cos^2x-sin^2x)=(cos^2x-sin^2x)
(cos^2x-sin^2x)=cos2x
b)
5cos^2x + 2sin^2x = 4 \\ 5 \frac{cos^2x}{sin^2x}+2= \frac{4}{sin^2x}   \\ 5cot^2x+2=4cosec^2x
cot^2x+2=4(cosec^2x-cot^2x)=4
(cosec^2x-cot^2x)=1 formula
cot^2x=2
cot x= \frac{1}{tan x} formula
tan^2x= \frac{1}{2}




0
2014-04-01T18:38:22+05:30
A) Prove that for all values of x : (cos^4)x - (sin^4)x = (cos^2)x - (sin^2)x 
LHS+(cos^4)x - (sin^4)x=(cos²x)² - (sin²x)²
=(cos²x+sin²x)(cos²x - sin²x)
=(1)(cos²x - sin²x) =cos²x - sin²x =RHS
b) Given that 5(cos^2)x + 2(sin^2)x = 4, show that (tan^2)x = 1/2 
 5cos²x + 2sin²x =4
→3cos²x+2cos²x+ 2sin²x=4
→  3cos²x+2(cos²x+ sin²x)=4
→  3cos²x+2=4  or 3cos²x=2
i.e cos²x=2/3
and sin²x=1−cos²x =1−(2/3)=1−2/3 =1/3
Hence tan²x=sin²x/cos²x =(1/3)/(2/3)=1/2

0
please note cos^2x=2/3
u squared it again
sin^2x=1/3
tan^2x=sin^2 x/cos^2 x=(1/3)/(2/3)=1/2