Question

Hello friends !!!
Good afternoon !!
Answer the question which is in the given pic .!!!

Answer 1

Good Afternoon,
Hey! Here is your answer.

Concepts / Identities to know :

1) Quadratic form and its relation between roots.
Like :

Sum of Roots
Product of roots

2) Trigonometric Identities :

cos a = (1 - tan ^(a/2))/(1+tan ^(a/2))

sin a = 2 tan a/2 /(1 + tan ^ (a/2)):

Steps:

1) Make Quadratic in sin (theta. )
For a) and b) Part.

For a)

Do Sum of Roots in quadratic form of sin theta.

For b)

DO product of roots in quadratic form of sin theta

Then, do sum of roots and Product of roots.

2) Make Quadratic in tan (theta/2 )
Then same as above..

For c) and d) Part.

For Calculation see Pic attached to it.

Now, For Calculation see pic.

Hope, you understand my answer :

If not, then tell me :

Answer 2

Step-by-step explanation:

From the given relation, we have

acosθ=c−bsinθ

Square and change in terms of sinθ

a2(1−sin2θ)=c2−2bcsinθ+b2sin2

∴(a2+b2)sin2θ−2bcsinθ+(c2−a2)=0

Its roots are sinα and sinβ as α and β are the values of θ as given

∴sinα+sinβ=a2+b22bc (Sum of roots)

sinαsinβ=a2+b2c2−a2 (product of roots)