In a class, teacher gave a statement: sinA + cos B =x, cosA - sinB =y. Then Ajit came forward saying that $x^{2} + y^{2} = 2$ . What can be said about Ajit's statement?

Always true

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Always false

No worries! We‘ve got your back. Try BYJU‘S free classes today!

True in some cases

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Can't say

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A
Always true

sinA + cos B= x ------- (i)

cosA - sinB= y ------ (ii)

Squaring (i) and (ii) and adding we get

$x^{2} + y^{2} = 2$ . So, Ajit's statement will always be true.

Suggest Corrections

Similar questions

\frac{sin A - sin B}{cos A + cos B} + \frac{cos A - cos B}{sin A + sin B} = 0

$\frac{s i n A - s i n B}{c o s A + c o s B} + \frac{c o s A - c o s B}{s i n A + s i n B} =$

Simplify the expression:
$\frac{s i n A - s i n B}{c o s A + c o s B} + \frac{c o s A - c o s B}{s i n A + s i n B}$

sin A = sin B

cos A = cos B

sin \frac{A - B}{2} =

{(\frac{cos A + cos B}{sin A - sin B})}^{n} + {(\frac{sin A + sin B}{cos A - cos B})}^{n}

= 2 {cot}^{n} (\frac{A - B}{2})

n

= 0

n

\frac{cos A + cos B}{sin A - sin B} = cot \frac{A - B}{2}

Join BYJU'S Learning Program