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We know that
sin
2
x + cos
2
x = 1
We can write it as
cos
2
x = 1 – sin
2
x
We know that
1 + tan
2
x = sec
2
x
We can write it as
1 + (4/3)
2
= sec
2
x
Substituting the values
1 + 16/9 = sec
2
x
cos
2
x = 25/9
sec x = ± 5/3
Here x lies in the third quadrant, so the value of sec x will be negative
sec x = – 5/3
We can write it as
We know that
sin
2
x + cos
2
x = 1
We can write it as
sin
2
x = 1 – cos
2
x
Substituting the values
sin
2
x = 1 – (5/13)
2
sin
2
x = 1 – 25/169 = 144/169
sin
2
x = ± 12/13
Here x lies in the fourth quadrant, so the value of sin x will be negative
sin x = – 12/13
We can write it as
We know that
1 + tan
2
x = sec
2
x
We can write it as
1 + (-5/12)
2
= sec
2
x
Substituting the values
1 + 25/144 = sec
2
x
sec
2
x = 169/144
sec x = ± 13/12
Here x lies in the second quadrant, so the value of sec x will be negative
sec x = – 13/12
We can write it as
By further calculation
= sin 45
o
= 1/
√
2
By further calculation
= cosec 30
o
= 2
By further calculation
We get
= tan 60
o
=
√
3
By further calculation
By further calculation
