Advertisements
Advertisements
Question
If 4 sin2 θ – 1 = 0 and angle θ is less than 90°, find the value of θ and hence the value of cos2 θ + tan2 θ.
Advertisements
Solution
4 sin2 θ – 1 = 0
sin2 θ = `(1)/(4)`
sin θ = `(1)/(2)`
sin θ = sin 30°
θ = 30°
cos2 θ + tan2 θ = cos2 30° + tan2 30°
= `(sqrt(3)/2)^2 + ( 1/sqrt(3))^2`
= `(3)/(4) + (1)/(3)`
= `(9 + 4)/(12)`
= `(13)/(12)`
RELATED QUESTIONS
Solve for x : sin (x + 10°) = `(1)/(2)`
Find the value of 'A', if `sqrt(3)cot"A"` = 1
If θ = 30°, verify that: tan2θ = `(2tanθ)/(1 - tan^2θ)`
If A = B = 60°, verify that: tan(A - B) = `(tan"A" - tan"B")/(1 + tan"A" tan"B"")`
If θ < 90°, find the value of: `tan^2θ - (1)/cos^2θ`
Find the value of: `sqrt((1 - sin^2 60°)/(1 + sin^2 60°)` If 3 tan2θ - 1 = 0, find the value
a. cosθ
b. sinθ
Find the value 'x', if:
Evaluate the following: `(sec34°)/("cosec"56°)`
Evaluate the following: sin28° sec62° + tan49° tan41°
If sec2θ = cosec3θ, find the value of θ if it is known that both 2θ and 3θ are acute angles.
