Question

If sinA + cosA = a then,find the value of sinA/secA ?​

Answer 1

Answer:

( a^2 - 1 ) / 2

Step-by-step explanation:

⇒ sinA + cosA = a

  Square on both sides :

⇒ ( sinA + cosA )^2 = a^2

⇒ sin^2 A + cos^2 A + 2sinA.cosA = a^2

    sin^2 A + cos^2 A = 1

⇒ 1 + 2 sinA.cosA = a^2

     cosA = 1/secA

⇒ 2 sinA( 1/ secA ) = a^2 - 1

⇒ sinA/secA = ( a^2 - 1 ) / 2

   Hence the required value is ( a^2 - 1 ) / 2

Answer 2

GIVEN:

sinA + cosA = a

TO FIND:

• sinA/secA

SOLUTION:

sinA + cosA = a

Squaring on both sides

( sinA + cosA )² = a²

Simplifying using

(a + b)² = a² + 2ab + b²

sin²A + 2sinAcosA + cos²A = a²

We know that

sin²A + cos²A = 1

And substituting cosA = 1/secA

→ 1 + 2sinA/secA = a²

→ sinA/secA = a² - 1/2

Hence, sinA/secA = (a² - 1)/2