Question

If 3cos teeta = 1 ,find the value of 6sin² teeta + tan ²teeta /4cos² teeta

Answer 1

Given : 3 cos theta = 1 so cos theta = 1/3

******* We know sin^2 theta + cos^2 theta = 1

so sin^2 theta + ( 1/3)^2 = 1

Sin^2 theta + (1/9)= 1

Sin^2 theta = 1- 1/9

Sin^2 theta = (9-1)/9 = 8/9

****** We know tan theta = Sin theta / cos theta

tan^2 theta = sin^2 theta/ cos^2 theta

= (8/9 ) /( 1/9 )

= 8

Now we place values of sin^2 theta and tan^2 theta in given expression

6 ( 8/9 ) + 8 (48/9) + 8 48 + 72

--------------------------------- = -------------------- = -------------------------

4 ( 1/9) 4/9 4

120/4 = 30

Answer 30