Question

(Sin^2a-3Sina+2)÷cos^2a=1 then a=?

Answer 1

Concept:

Trigonometry is a discipline of mathematics that investigates the relationship between triangle side lengths and angles.

Given:

$\frac{sin^{2} a-3sina+2}{cos^{2} a} =1$

To find:

The value of a

Solution:

This question is about trigonometry

Here, an equation is given to us$\frac{sin^{2} a-3sina+2}{cos^{2}a } =1$

And we have to find the value of a

So to find the value we first have to take the denominator to the right-hand side

so we get,

$sin^{2} a-3sina+2=cos^{2}a$

Also, we know that $sin^{2} a+ cos^{2}a=1$

so on the right-hand side, we can write $1-sin^{2}a$

so the equation becomes

$sin^{2} a-3sina+2=1-sin^{2} a\\2sin^{2}a-3sina+1=0\\2sin^{2} a-2sina. sina+1=0\\sina(sina-1)-1(sina-1)=0\\sina=1,\frac{1}{2}$

Now, we get two values of a by solving the equation

a=1, 1/2

we know that

$sin 40=1\\sin30=\frac{1}{2}$

So we can write a= 40°, 30°

#SPJ2

Answer 2

Step-by-step explanation:

the required angle is 30°