Question

Choose the correct option :

1) 2tan30° / 1 + tan^230° =
A) sin60° B) cos60° C) tan60° D) sin30°

2) 1 - tan^2 45° / 1 + tan^2 45°
A) tan90° B) 1 C) sin45° D) 0

3) sin2A = 2sinA is true when A =
A) 0° B) 30° C) 45° D) 60°

Answer 1

Question 1 :-

2tan30° / 1 + tan²30° =

a) sin60°

b) cos60°

c) tan60°

d) sin30°

Answer :

• a) sin60°

Explanation :

⇒ 2tan30° / 1 + tan²30°

⇒ 2 (1 / √3) / 1 + (1 / √3)²

⇒ (2 / √3) / 1 + 1 / 3

⇒ (2 / √3) / (4 / 3)

⇒ 2 / √3 × 3 / 4

⇒ 2 / √3 × √3 × √3 / 2 × 2

⇒ √3 / 2

⇒ sin60°

Hence,

Option (a) sin60° is correct.

________________

Question 2 :-

1 - tan²45° / 1 + tan²45°

a) tan90°

b) 1

c) sin45°

d) 0

Answer :

• d) 0

Explaination :

⇒ 1 - tan²45° / 1 + tan²45°

⇒ 1 - (1)² / 1 + (1)²

⇒ 1 - 1 / 1 + 1

⇒ 0 / 2

⇒ 0

________________

Hence,

Option (d) 0 is correct.

Question 3 :-

sin2A = 2sinA is true when A =

a) 0°

b) 30°

c) 45°

d) 60°

Answer :

• a) 0°

Explaination :

⇒ sin2A = 2sinA

⇒ sin2 (0°) = 2sin (0°)

⇒ sin0° = 2sin0°

⇒ 0 = 0

Hence,

Option a) 0° is correct.

Answer 2

Question 1 :-

${\sf{\green{2tan30° / 1 + tan²30° =>}}}$

${\bold{\sf\green{a) sin60°}}}$

${\bold{\sf{\green{b) cos60°}}}}$

${\bold{\sf\green{c) tan60°}}}$

${\bold{\sf\green{d) sin30°}}}$

Answer :

a) sin60°

Explanation :

${\bold{\sf\red{⇒ 2tan30° / 1 + tan²30°}}}$

${\bold{\sf\red{⇒ 2 (1 / √3) / 1 + (1 / √3)²}}}$

${\bold{\sf\red{⇒ (2 / √3) / 1 + 1 / 3}}}$

${\bold{\sf\red{⇒ (2 / √3) / (4 / 3)}}}$

${\bold{\sf\red{⇒ 2 / √3 × 3 / 4}}}$

${\bold{\sf\red{⇒ 2 / √3 × √3 × √3 / 2 × 2}}}$

${\bold{\sf\red{⇒ √3 / 2}}}$

${\bold{\sf\red{⇒ sin60°}}}$

Hence,

Option (a) sin60° is correct.

____________________

Question 2 :-

${\bold{\sf\purple{1 - tan²45° / 1 + tan²45°}}}$

${\bold{\sf\purple{a) tan90° }}}$

${\bold{\sf\purple{b) 1 }}}$

${\bold{\sf\purple{c) sin45° }}}$

${\bold{\sf\purple{d) 0}}}$

Answer :

d) 0

Explaination :

${\bold{\sf\pink{⇒ 1 - tan²45° / 1 + tan²45°}}}$

${\bold{\sf\pink{⇒ 1 - (1)² / 1 + (1)²}}}$

${\bold{\sf\pink{⇒ 1 - 1 / 1 + 1}}}$

${\bold{\sf\pink{⇒ 0 / 2}}}$

${\bold{\sf\pink{⇒ 0}}}$

____________________

Hence,

Option (d) 0 is correct.

Question 3 :-

${\bold{\sf\blue{sin2A = 2sinA is true when A = }}}$

${\bold{\sf\blue{a) 0° }}}$

${\bold{\sf\blue{b) 30° }}}$

${\bold{\sf\blue{c) 45° }}}$

${\bold{\sf\blue{d) 60°}}}$

Answer :

a) 0°

Explaination :

${\bold{\sf\orange{⇒ sin2A = 2sinA}}}$

${\bold{\sf\orange{⇒ sin2 (0°) = 2sin (0°)}}}$

${\bold{\sf\orange{⇒ sin0° = 2sin0°}}}$

${\bold{\sf\orange{⇒ 0 = 0}}}$

Hence,

Option a) 0° is correct.

____________________