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

If A + B + C = 180°, prove that cos A + cos B − cos C = `- 1 + 4cos  "A"/2 cos  "B"/2 sin  "C"/2`

If A + B + C = 180°, prove that sin²A + sin²B + sin²C = 2 + 2 cos A cos B cos C

If A + B + C = 180°, prove that sin²A + sin²B − sin²C = 2 sin A sin B cos C

If A + B + C = 180°, prove that `tan  "A"/2  tan  "B"/2 + tan  "B"/2 tan  "C"/2 + tan  "C"/2 tan  "A"/2` = 1

If A + B + C = 180°, prove that sin A + sin B + sin C = `4 cos  "A"/2 cos  "B"/2 cos  "C"/2`

If A + B + C = 180°, prove that sin(B + C − A) + sin(C + A − B) + sin(A + B − C) = 4 sin A sin B sin C

If A + B + C = 2s, then prove that sin(s – A) sin(s – B)+ sin s  sin(s – C) = sin A sin B

If x + y + z = xyz, then prove that `(2x)/(1 - x^2) + (2y)/(1 - y^2) + (2z)/(1 - z^2) = (2x)/(1 - x^2) (2y)/(1 - y^2) (2z)/(1 - z^2)`

If A + B + C = `pi/2`, prove the following sin 2A + sin 2B + sin 2C = 4 cos A cos B cos C

If A + B + C = `pi/2`, prove the following cos 2A + cos 2B + cos 2C = 1 + 4 sin A sin B sin C

If ∆ABC is a right triangle and if ∠A = `pi/2` then prove that cos² B + cos² C = 1

If ∆ABC is a right triangle and if ∠A = `pi/2` then prove that sin² B + sin² C = 1

If ∆ABC is a right triangle and if ∠A = `pi/2` then prove that cos B – cos C = `- 1 + 2sqrt(2) cos  "B"/2  sin  "C"/2`

Choose the correct alternative:
`1/(cos 80^circ) - sqrt(3)/(sin 80^circ)` = 

Choose the correct alternative:
If cos 28° + sin 28° = k³, then cos 17° is equal to

Choose the correct alternative:
`(1 + cos  pi/8) (1 + cos  (3pi)/8) (1 + cos  (5pi)/8) (1 + cos  (7pi)/8)` =

Choose the correct alternative:
If `pi < 2theta < (3pi)/2`, then `sqrt(2 + sqrt(2 + 2cos4theta)` equals to

Choose the correct alternative:
cos 1° + cos 2° + cos 3° + ... + cos 179° =

Choose the correct alternative:
Let fk(x) = `1/"k" [sin^"k" x + cos^"k" x]` where x ∈ R and k ≥ 1. Then f₄(x) − f₆(x) = 

Choose the correct alternative:
`(sin("A" - "B"))/(cos"A" cos"B") + (sin("B" - "C"))/(cos"B" cos"C") + (sin("C" - "A"))/(cos"C" cos"A")` is