if tan theta = root 3 then find the value of sin thera & sec theta where pie less than equal to theta & 3pie/2 greater than equal to theta
Answers
Step-by-step explanation:
we know that
tanθ=
sideadjacenttoangleθ
sideoppositetoangleθ
ortanθ=
Base
Perpendicular
Given: tanB=
3
tanB=
1
3
tanB=
1
3
⇒
B
P
=
1
3
⇒
AB
AC
=
1
3
Let
side opposite to angle B=AC=
3
k
side adjacent to angle B=aB=1k
where k is any positive integer
Firstly we have to find the value of BC
so we can find the value of AC with help of Pythagoras theorem.
⇒(AB)
2
+(AC)
2
=(BC)
2
⇒(1k)
2
+(
3
k)
2
=(BC)
2
⇒(BC)
2
=1k
2
+3k
2
⇒(BC)
2
=4k
2
⇒BC=
4k
2
=±2k
but side can't be negative so, BC=2k
Now we will find sinB and cosB
we know that
sinθ=
hypotenuse
sideoppositetoangleθ
side opposite to angle B=AC=k
3
Hypotenuse =BC=2k
so, sinB=
BC
AC
=
2k
3
k
=
2
3
Now we know that
cosθ=
hypotenuse
sideadjacenttoangleθ
side adjacent to angle B=AB=1k
Hypotenuse =BC=2k
So, cosB=
BC
AB
=
2k
1k
=
2
1
Answer:
tan theta = √3/√3×√3
than theta =1/√3
which is 30
so theta value is 30 when u put the value in equation then u will be available to find the answer