cos 15 - tan 15 value
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Find the Values of Sin 15, cos 15 ,tan 15 ,sin 75, cos 75 ,tan 75
November 5, 2019 by physicscatalyst Leave a Comment
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Values of Sin 15, cos 15 ,tan 15 ,sin 75, cos 75 ,tan 75 of degrees can be easily find out using the trigonometric identities. Also there can be many ways to find out the values. Lets explore few ways
Value of sin 15 degrees
Method 1 ( using sin 30)
(sin
A
2
+cos
A
2
)2=sin2
A
2
+cos2
A
2
+2sin
A
2
cos
A
2
Now sin2
A
2
+cos2
A
2
and sinA=2sin
A
2
cos
A
2
Therefore
(sin
A
2
+cos
A
2
)2=1+sinA
sin
A
2
+cos
A
2
=±
√
1+sinA
Similarly
(sin
A
2
–cos
A
2
)2=sin2
A
2
+cos2
A
2
–2sin
A
2
cos
A
2
or
sin
A
2
–cos
A
2
=±
√
1–sinA
Now putting A= 30, we get
sin15+cos15=±
√
1+sin30
and
sin15–cos15=±
√
1–sin30
Now we know that sin 15 > 0 and cos 15 > 0,
Therefore
sin15+cos15=
√
1+sin30
=
√
3
√
2
-(1)
But we are not sure about the values of sin 15 – cos 15
Lets see how to determine it
sin15–cos15=
√
2
(
1
√
2
sin15–
1
√
2
cos15)
=
√
2
(cos45sin15–sin45cos15)=
√
2
sin(15−45)=–
√
2
sin30
So it is a negative
sin15–cos15=–
√
1–sin30
=–
1
√
2
-(2)
Adding (1) and (2), we get
2sin15=
√
3
√
2
–
1
√
2
sin15=
√
3
−1
2
√
2
Step-by-step explanation:
The answer is zero.
As done above.
