Question

6. If cos X = ⅔ then tan X is equal to: (a)5/2 (b)√(5/2) (c)√5/2 (d)2/√5

Answer 1

6. If cos X = ⅔ then tan X is equal to:

(a)5/2

(b)√(5/2)

(c)√5/2☺️ ☺️

(d)2/√5

Answer: (c)

Explanation: By trigonometry identities, we know:

1+tan2X=sec2X

And sec X = 1/cos X = 1/(⅔) = 3/2

Hence,

1+tan2X=(3/2)2=9/4

tan2X=9/4-1=5/4

Tan X = √5/2

Answer 2

secx = 1/cosx = 3/2

Use the identity sec²x = 1 + tan²x

(3/2)² = 1 + tan²x

tan²x = 9/4 - 1

tan²x = 5/4

tanx = rt5 / 2

Hence , option (c) is correct

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