Question

If root 3 tan theta = 3 sin theta, then the value of sin² theta - cos² theta

(a) 3
(b) 2/root 3
(c) ⅓
(d) -1 ​

Answer 1

Answer:

C) 1/3

Step-by-step explanation:

Given,

√3tanA = 3sinA

To Find :-

the values of :-

sin²A - cos²A

Solution :-

√3tanA = 3sinA

√3(sinA/cosA) = 3sinA

√3sinA/3sinA = cosA

1/√3 = cosA

→ cosA = 1/√3

Adj side/hyp side = 1/√3

→ Adj side = 1 , hyp side = √3

→ (hyp side)² = (adj side)²+(opp side)²

(√3)² = (1)²+(opp side)²

→(opp side)² = 2

opp side = √2

→ sinA = opp side/hyp side

= √2/√3

→ sin²A - cos²A

= (√2/√3)² - (1/√3)²

= 2/3 - 1/3

= 1/3

Therefore , sin²A - cos²A = 1/3.

Answer 2

Answer:

c) 1/3

Step-by-step explanation:

Given: √3 tanØ = 3 sinØ

To find: sin²Ø - cos²Ø

Solution:

We know that, secØ = √3 and cosØ = 1/√3

Now,

sin²Ø - cos²Ø = 1 - cos²Ø - cos²Ø

{ As sin²Ø = 1 - cos²Ø}

As cosØ = 1/√3, so cos²Ø = (1/√3)² = 1/3

Substitute the values,

→ 1 - 1/3 - 1/3

→ (3 - 1 - 1)/3

→ 1/3

Hence, the value of sin²Ø - cos²Ø is 1/3.