if tan theta = 1 find the value of (sec theta + cosec theta)^2
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Answer:
tanθ=1
⇒θ=
4
π
,π+
4
π
For θ=
4
π
cosθ+sinθ
secθ+cscθ
=
cos
4
π
+sin
4
π
sec
4
π
+csc
4
π
=
2
1
+
2
1
2
+
2
=
2
2
2
2
=2
2
×
2
2
=2
For θ=π+
4
π
cosθ+sinθ
secθ+cscθ
=
cos(π+
4
π
)+sin(π+
4
π
)
sec(π+
4
π
)+csc(π+
4
π
)
=
−cos
4
π
−sin
4
π
−sec
4
π
−csc
4
π
=
2
−1
−
2
1
−
2
−
2
=
2
−2
−2
2
=−2
2
×
2
−
2
=2
∴
cosθ+sinθ
secθ+cscθ
=2
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