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Question
If
s
e
c
θ
+
tan
θ
=
x
,
t
h
e
n
tan
θ
i
s
-
(
x
2
+
1
)
/
x
(
x
2
-
1
)
/
x
(
x
2
+
1
)
/
2
x
(
x
2
-
1
)
/
2
x
ANSWER : 4
Descrption
<p>Step - by - step explanation:</p> <p>Given : sec θ + tan θ = x …….. (1)</p> <p>By using an identity , sec² θ - tan² θ = 1</p> <p>(sec θ + tan θ)(sec θ - tan θ) = 1</p> <p>[By using identity , a² - b² = (a + b) (a - b) ]</p> <p>x (sec θ - tan θ) = 1</p> <p>(sec θ - tan θ) = 1/x ……….(2)</p> <p>On Subtracting eq 1 & 2, </p> <p>sec θ + tan θ - (sec θ - tan θ) = (x - 1/x)</p> <p>sec θ + tan θ - sec θ + tan θ) = (x - 1/x)</p> <p>2 tan θ = (x - 1/x)</p> <p>2 tan θ = (x² - 1)/x</p> <p>tan θ = (x² - 1)/2x</p> <p>Hence, the value of tan θ is (x² - 1)/2x.</p> <p> </p>
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