Question

tan 60°, cot45°, tan 30° are in A) A.PB) G.PC) H.PD) S.P​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

tan 60°, cot 45°, tan 30° are in

A) A.P

B) G.P

C) H.P

D) S.P

CONCEPT TO BE IMPLEMENTED

Three terms a, b, c are said to be in GP ( Geometric Progression) if

$\sf{ {b}^{2} = ac}$

EVALUATION

Here the given terms are tan 60°, cot45°, tan 30°

Now

$\tan {60}^{ \circ} = \sqrt{3}$

$\displaystyle \cot {45}^{ \circ} = 1$

$\displaystyle \tan {30}^{ \circ} = 1$

Therefore

$\displaystyle {\cot}^{2} {45}^{ \circ} = 1$

And

$\displaystyle \tan {60}^{ \circ} \times \tan {30}^{ \circ}$

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

$= 1$

$\therefore \: \: \displaystyle {\cot}^{2} {45}^{ \circ} = \tan {60}^{ \circ} \times \tan {30}^{ \circ}$

Hence tan 60°, cot 45°, tan 30° are in GP

FINAL ANSWER

tan 60°, cot 45°, tan 30° are in

B) G.P

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