Q) sec
+tan
=100,find the value of tan
+cot
Since, sec
+tan
=100
or 1+ sin
= 100cos
Squaring both the sides
(1+ sin
)(1+ sin
)= 10000 (cos
)((cos
or (1+ sin
)(1+ sin
)= 10000(1 - s
in2
)or (1+ sin
)(1+ sin
)= 10000(1 - s
in)(1 + sin)or (1+ sin ) = 10000(1 - sin) or sin = 9999/10001 (1) therefore cos =[(1 -
(9999/10001)2]1/2= (200/10001) (2) now ,
tan+cot =sin/cos + cos/sin = 1/sincos sustituting the values of sin and cos from (1) and (2) we obtain, tan
+cot
= (10001)
2/[9999
×200]
Moderation Team
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