Which one of the following is possible ?

Question

Which one of the following is possible ? (A)  cos θ = (7/3)  (B)  sin θ = (a2+b2/a2-b2) (a ≠ b) (C)  sec θ = (4/5) (D)  tan θ =45

Tardigrade Admin · Accepted Answer

(a) Suppose a=2, b=1 sin θ=(22+12/22-1)=(5/3)>1, which is not possible. (b) sec θ=(4/5)<1, which is not possible. (c) tan θ=45, which is possible. (d) cos θ=(7/3)>1, which is not possible.

Q. Which one of the following is possible ?

$cos θ = \frac{7}{3}$

$sin θ = \frac{a ^{2} + b ^{2}}{a ^{2} - b ^{2}} (a \neq = b)$

$sec θ = \frac{4}{5}$

$tan θ = 45$

(a) Suppose $a = 2, b = 1$
$sin θ = \frac{2 ^{2} + 1 ^{2}}{2 ^{2} - 1} = \frac{5}{3} > 1$ , which is not possible.
(b) $sec θ = \frac{4}{5} < 1$ , which is not possible.
(c) $tan θ = 45$ , which is possible.
(d) $cos θ = \frac{7}{3} > 1$ , which is not possible.

Q. Which one of the following is possible ?

cosθ=37​

sinθ=a2−b2a2+b2​(a=b)

secθ=54​

tanθ=45

(a) Suppose a=2,b=1 sinθ=22−122+12​=35​>1, which is not possible. (b) secθ=54​<1, which is not possible. (c) tanθ=45, which is possible. (d) cosθ=37​>1, which is not possible.

$cos θ = \frac{7}{3}$

$sin θ = \frac{a ^{2} + b ^{2}}{a ^{2} - b ^{2}} (a \neq = b)$

$sec θ = \frac{4}{5}$

$tan θ = 45$

(a) Suppose $a = 2, b = 1$
$sin θ = \frac{2 ^{2} + 1 ^{2}}{2 ^{2} - 1} = \frac{5}{3} > 1$ , which is not possible.
(b) $sec θ = \frac{4}{5} < 1$ , which is not possible.
(c) $tan θ = 45$ , which is possible.
(d) $cos θ = \frac{7}{3} > 1$ , which is not possible.