If sec x = √2and lies in 4 quadrant, Find the value of 1+tan x+ cosec x / 1+cot x-cosec x .
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Answer:
It is given that,
sec
x
=
2
we know,
cos
x
=
1
sec
x
⇒
cos
x
=
1
2
by the identity,
sin
2
x
+
cos
2
x
=
1
sin
2
x
=
1
−
(
1
2
)
2
⇒
sin
x
=
√
3
2
we know,
sin
x
=
1
csc
x
⇒
csc
x
=
2
√
3
by definition,
tan
x
=
sin
x
cos
x
⇒
tan
x
=
√
3
2
×
2
=
√
3
we know,
cot
x
=
1
tan
x
⇒
cot
x
=
1
√
3
now,
cot
x
+
csc
x
=
1
√
3
+
2
√
3
=
3
√
3
=
√
3
Step-by-step explanation:
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