If cos-1p + cos-1q + cos-1r = π, then p2 + q2 + r2 + 2pqr is equal to
3
1
2
- 1
If sin-1x5 + csc-154 = π2, then x is equal to
4
5
sin12cos-145
- 110
110
If cos-1x + cos-1y + cos-1z = 3π, then xy + yz + zx is equal to
0
- 3
If tan-1x + 1x - 1 + tan-1x - 1x = tan-1- 7, then the value of x is
zero
- 2
If cos-1p + cos-11 - p + cos-11 - q = 3π4, then the value of q is
22
1/2
1/3
The soluton of sin-1x - sin-12x = ± π3 is
± 13
± 14
± 32
± 12
D.
sin-1x - sin-12x = ± π3⇒ sin-1x - sin-1± 32 = sin-12x⇒ sin-1x1 - 34 - ± 321 - x2 = sin-12x⇒ x2 - ± 321 - x2 = 2x⇒ - ± 31 - x2 = 3xOn squaring both sides, we get 31 - x2 = 9x2⇒ 1 - x2 = 3x2⇒ 4x2 = 1⇒ x = ± 12
If cos-1x = α, 0 < x < 1 and sin-12x1 - x2 + sec-112x2 - 1 = 2π3, then tan-12x equals :
π6
π4
π3
π2
If a > b > 0, then the value of tan-1ab + tan-1a + ba - b depends on :
both a and b
b and not a
a and not b
neither a nor b
The solution of tan-1x + 2cot-1x = 2π3 is
- 13
13