Question

If x = a sin θ and y = a cos θ then find the value of x² + y².

Answer 1

Trigonometry is the study of the relationship between the sides and angles of a triangle.

An equation involving trigonometry ratios of an angle is called is called a trigonometric  identity, if it is true for all values of the angles involved. For any acute angle θ, we have 3 identities.

i) sin² θ + cos² θ = 1 ,ii) 1 + tan² θ = sec² θ , iii) cot² θ +1 = cosec² θ.

SOLUTION:

GIVEN:
x = a sin θ &  y = a cos θ
x² + y²

On Putting the value of x & y

x² + y²  = (a sin θ)² + (a cos θ)²
= a²sin² θ + a² cos² θ

= a² ( sin² θ + cos²θ)
= a² (1)

[sin² θ + cos² θ = 1]
x² + y²  = a²

Hence, the value of x² + y² is a².

HOPE THIS WILL HELP YOU...

Answer 2

Theta is written as @

x² =(a * sin@)²

y² = (a * cos@)²

Now,

x²+y² =(a*sin@)² + (a*cos@)²

As "a²" is common in both,

Then,

x²+y² = a²(sin²@ + cos²@)

______________________________

SOLVING sin²@ + cos²@

Sin²@ =(hieght/hypotenuse)²

And

Cos²@ =(base/hypotenuse)²

Then,

Sin²@ + cos²@ = (base² + hieght²)/hypotenuse²

Sin²@ + cos²@ =(hypotenuse²)/(hypotenuse²)

Sin²@ + cos²@ =1

Value of sin²@ + cos²@ is 1
______________________________

Now,

Continue,

a²(sin²@ + cos²@)

=a²*1

=a²

x²+y² =a²

I hope this will help you

-by ABHAY