Question

7sin^2 +3cos^2=4 show that tan =1÷root3

Answer 1

7sin2 +3cos2 =4
7sin2 + 3(1-sin2)=4
7sin2 +3-3sin2 =4
4sin2=4-3
4sin2 =1
sin2 =1/4
sin= 1/2
sin = P/H. (P=perpendicular,H=hypotenuse)
By pythagoras theorem
P2 +B2 =H2
H2 - P2 = B2
(2)2 - (1)1 =B2
4 - 1 =3
B2 = 3
B= root3
cos = root 3/2
tan = sin/cos
= (1/2)/(√3/2)
=1/√3. Hence proved

Answer 2

Hiii friend,

7Sin² theta + 3Cos² theta = 4


LHS = 7Sin² theta + 3 Cos²theta


=> 4Sin²theta + 3Sin²theta + 3Cos²theta


=> 4Sin²theta + 3(Sin²theta+Cos²theta)

=> 4 Sin²theta + 3 × 1


=> 4 Sin²theta + 3


Now LHS = RHS


4 Sin²theta + 3 = 4


4 Sin²theta = 4-3


4Sin²theta = 1


Sin²theta = 1/4


Therefore,

Cos²theta = (1-Sin²theta) = (1-1/4) = 3/4


Tan²Theta = Sin²theta/Cos²theta = (1/4 × 3/4) = 1/3



Tan²Theta = 1/3


Tan Theta = ✓1/3 = 1/✓3....... PROVED.....



HOPE IT WILL HELP YOU......... :-)