Question

sin30° x tan 30° x cot 30° x cosec 60° =..
(A) tan 30°
(B) cot 60°
(C) sin 30° x cosec 60°
(D) All of the above
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Answer 1

Sin30° x tan 30° x cot 30° x cosec 60°

$=\frac{1}{2}\times\frac{1}{\sqrt{3}}\times\sqrt{3}\times\frac{2}{\sqrt{3}}$

$=\frac{1}{\sqrt{3}}$

Verifying the options given:

(A) tan 30° $=\frac{1}{\sqrt{3}}$

(B) cot 60° $=\frac{1}{\sqrt{3}}$

(C) sin 30° x cosec 60°

$=\frac{1}{2}\times\frac{2}{\sqrt{3}}$

$=\frac{1}{\sqrt{3}}$

$\therefore$ The correct answer

is (D) All of the above

Answer 2

tan 30°

Step-by-step explanation:

$sin30 \times tan30 \times cot30 \times cosec60$

$=1/2 \times 1/\sqrt3 \times \sqrt3 \times 2/\sqrt{3}$

=1/√3

=tan 30°