Which of the following is incorrect?(a) sin x = −1/5(b) cos x = 1(c) sec x = 1/2(d) tan x = 20

Question

\[ \text{Which of the following is incorrect?} \]

(a) \(\sin x=-\frac15\)
(b) \(\cos x=1\)
(c) \(\sec x=\frac12\)
(d) \(\tan x=20\)

We know that

\[ -1\le\sin x\le1 \]

\[ -1\le\cos x\le1 \]

So options (a) and (b) are possible.

Also,

\[ \tan x \]

can take any real value, so option (d) is possible.

But

\[ \sec x=\frac1{\cos x} \]

Since

\[ -1\le\cos x\le1 \]

therefore

\[ \sec x\le-1 \quad \text{or} \quad \sec x\ge1 \]

Hence

\[ \sec x=\frac12 \]

is not possible.

\[ \boxed{\sec x=\frac12} \]

Correct Option: (c)

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