If a-cos-cos-sin-sin-cos- b-cos-sin-sin-cos-cos-and c-sin-sin- then a2-b2-c2 is equal to

You visited us 8 times! Enjoying our articles? Unlock Full Access!

Trigonometric Identities

If a=cosαco...

Question

If $a = cos α cos β + sin α sin β cos γ$
$b = cos α sin β - sin α cos β cos γ$
and $c = sin α sin γ$ , then $a^{2} + b^{2} + c^{2}$ is equal to

- 1

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

0

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

1

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

none of these

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

Open in App

Solution

The correct option is C $1$
Given $a = cos α cos β + sin α sin β cos γ$
$b = cos α sin β - sin α cos β cos γ$
and $c = sin α sin γ$

Consider, $a^{2} + b^{2} + c^{2} = {cos}^{2} α {cos}^{2} β + {sin}^{2} α {sin}^{2} β {cos}^{2} γ + 2 cos α cos β sin α sin β cos γ + {cos}^{2} α {sin}^{2} β + {cos}^{2} β {sin}^{2} α {cos}^{2} γ - 2 cos α cos β sin α sin β c o s γ + 4 {sin}^{2} α {sin}^{2} γ$

$\Rightarrow a^{2} + b^{2} + c^{2} = {cos}^{2} α + {sin}^{2} α {cos}^{2} γ + 4 {sin}^{2} α {sin}^{2} γ$

$\Rightarrow a^{2} + b^{2} + c^{2} = 1 + 3 c^{2}$

Suggest Corrections

Similar questions

$I f a = c o s α c o s β + s i n α s i n β c o s γ, b = c o s α s i n β - s i n α c o s β c o s γ a n d c = s i n α s i n γ t h e n a^{2} + b^{2} + c^{2} i s e q u a l t o$

Q. If

a + b + c = 0

then

\frac{1}{b^{2} + c^{2} - a^{2}} + \frac{1}{c^{2} + a^{2} - b^{2}} + \frac{1}{a^{2} + b^{2} - c^{2}}

is equal to

Q. If three real numbers

a, b, c

none of which is zero are related by:

a^{2} = b^{2} + c^{2} - 2 b c \sqrt{1 - a^{2}}, b^{2} = c^{2} + a^{2} - 2 c a \sqrt{1 - b^{2}}, c^{2} = a^{2} + b^{2} - 2 a b \sqrt{1 - c^{2}}

, then prove that

a = c \sqrt{1 - b^{2}} + b \sqrt{1 - c^{2}}

I f ∣ ∣ a s i n^{2} θ + b s i n θ c o s θ + c c o s^{2} θ - \frac{1}{2} (a + c) ∣ ∣ \leq \frac{1}{2} k, t h e n k^{2} i s e q u a l t o

In any $△ A B C, \frac{1}{r_{1}^{2}} + \frac{1}{r_{2}^{2}} + \frac{1}{r_{3}^{2}} + \frac{1}{r^{2}}$ is equal to

Join BYJU'S Learning Program

If a=cosαcosβ+sinαsinβcosγb=cosαsinβ−sinαcosβcosγand c=sinαsinγ, then a2+b2+c2 is equal to

If $a = cos α cos β + sin α sin β cos γ$
$b = cos α sin β - sin α cos β cos γ$
and $c = sin α sin γ$ , then $a^{2} + b^{2} + c^{2}$ is equal to