Question

value of A =30 then prove that sinA = tan A /√1+tan^2A​

Answer 1

Step-by-step explanation:

Given :-

A = 30°

To find:-

If A =30° then prove that sinA = tan A /√1+tan^2A

Solution:-

Given that A = 30°

LHS:-

Sin A

=> Sin 30°

=> 1/2

LHS = 1/2 -------------------------(1)

RHS:-

tan A /√1+tan^2A

=> Tan 30° /√(1+ Tan^2 30°)

=> (1/√3) / √[1+ (1/√3)^2]

=> (1/√3)/√[1+(1/3)]

=> (1/√3) / √[(3+1)/3]

=> (1/√3) / √(4/3)

=>( 1/√3) / (2/√3)

=> (1/√3) × (√3/2)

=> √3/(√3 × 2)

=> 1/2

RHS= 1/2 ---------------------(2)

From (1)&(2)

LHS = RHS

sinA = tan A /√1+tan^2A

Answer:-

Verified the given realtion that

sinA = tan A /√1+tan^2A for A = 30°

Used formulae:-

• Sin 30°=1/2
• Tan 30°=1/√3