HSC Arts Class 11 - Tamil Nadu Board of Secondary Education Question Bank Solutions for Mathematics

Choose the correct alternative:
The number of roots of (x + 3)⁴ + (x + 5)⁴ = 16 is

Find the principal solution and general solution of the following:
sin θ = `-1/sqrt(2)`

Find the principal solution and general solution of the following:
cot θ = `sqrt(3)`

Find the principal solution and general solution of the following:
tan θ = `- 1/sqrt(3)`

Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°

sin⁴x = sin²x

Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°

2 cos²x + 1 = – 3 cos x

Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°

2 sin²x + 1 = 3 sin x

Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°

cos 2x = 1 − 3 sin x

Solve the following equations:
sin 5x − sin x = cos 3

Solve the following equations:
2 cos²θ + 3 sin θ – 3 = θ

Solve the following equations:
cos θ + cos 3θ = 2 cos 2θ

Solve the following equations:
sin θ + sin 3θ + sin 5θ = 0

Solve the following equations:
sin 2θ – cos 2θ – sin θ + cos θ = θ

Solve the following equations:
sin θ + cos θ = `sqrt(2)`

Solve the following equations:
`sin theta + sqrt(3) cos theta` = 1

Solve the following equations:
cot θ + cosec θ = `sqrt(3)`

Solve the following equations:
`tan theta + tan (theta + pi/3) + tan (theta + (2pi)/3) = sqrt(3)`

Solve the following equations:
cos 2θ = `(sqrt(5) + 1)/4`

Solve the following equations:
2cos ²x – 7 cos x + 3 = 0

Choose the correct alternative:
If tan 40° = λ, then `(tan 140^circ - tan 130^circ)/(1 + tan 140^circ *  tan 130^circ)` =