Question

HEYA..... ☺☺☺

.
.
.
» SOLVE IT

» FULL Explanation

»15 points

» don't answer if u dont know

Answer 1

Answer:

Option (A).

Explanation:

Given that tanA and tanB are the roots of the Equation x^2 - ax + b = 0.

It is in the form of ax^2 + bx + c = 0 ,

we get a = 1, b = -a, c = 1.

We know that sum of the roots = -b/a

= > tanA + tanB = -(-a)/1

                           = a



We know that product of roots = c/a

= > tan A * tanB = b/1

                           = 1.


Now,

We know that Tan(A + B) = tanA + tanB/1 - tanAtanB

                                          = a/1 - b


Note : We know that 1 + tan^2a = sec^2a = > tan^2a = sec^2a - 1.

Therefore :

Tan(A + B) = a/1 - b

Tan^2(A+ B) = a^2/1 - b^2

Sec^2(A + B) - 1 = a^2/1 - b^2

sec^2(A + B) = 1 + a^2/1 - b^2

Now,

Sin^2(A + B) = tan^2(A + B)/sec^2(A + B)

                     $= \frac{a^2}{ \frac{1 - b^2}{1 + \frac{a^2}{1 - b^2} } }$

                    $= \frac{a^2}{a^2 + (1 - b^2)}$




Hope this helps!

Answer 2

Hi,

Please see the attached file!


Thanks