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Byju's Answer
Standard IX
Mathematics
Calculating Heights and Distances
Sec theta(1-s...
Question
Sec theta(1-sin theta)(sec theta+ tan theta)=1
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Similar questions
Q.
Prove the following.
(1) secθ (1 – sinθ) (secθ + tanθ) = 1
(2) (secθ + tanθ) (1 – sinθ) = cosθ
(3) sec
2
θ + cosec
2
θ = sec
2
θ × cosec
2
θ
(4) cot
2
θ – tan
2
θ = cosec
2
θ – sec
2
θ
(5) tan
4
θ + tan
2
θ = sec
4
θ – sec
2
θ
(6)
1
1
-
sin
θ
+
1
1
+
sin
θ
=
2
sec
2
θ
(7) sec
6
x
– tan
6
x
= 1 + 3sec
2
x
× tan
2
x
(8)
tan
θ
s
e
c
θ
+
1
=
s
e
c
θ
-
1
tan
θ
(9)
tan
3
θ
-
1
tan
θ
-
1
=
sec
2
θ
+
tan
θ
(10)
sin
θ
-
cos
θ
+
1
sin
θ
+
cos
θ
-
1
=
1
sin
θ
-
tan
θ
Q.
Prove :
(tanθ + sinθ) / (tanθ - sinθ) = (secθ + 1) / (secθ - 1)
Q.
1
+
sin
θ
1
-
sin
θ
is equal to
(a) sec θ + tan θ
(b) sec θ − tan θ
(c) sec
2
θ + tan
2
θ
(d) sec
2
θ − tan
2
θ
