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
C.
We have, sin-1x5 + csc-154 = π2⇒ sin-1x5 + csc-154 = π2⇒ sin-1x5 × 1 - 452 + 451 - x52 = π2or x5 × 35 + 45 × 25 - x25 = sinπ2⇒ 3x + 425 - x2 = 25⇒ 425 - x2 = 25 - 3x
On squaring both sides, we get
16(25 - x2) = 625 + 9x2 - 150x
⇒ 4500 - 16x2 = 625 + 9x2 - 150x⇒ 16x2 + 9x2 - 150x + 625 - 400 = 0⇒ 25x2 - 150x + 225 = 0⇒ x2 - 6x + 9 = 0or x2 - 3x - 3x + 9 = 0 xx - 3 - 3x - 3 = 0 x - 32 = 0∴ x = 3
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
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