If (a^2 - b^2)sin x + 2abcos x = a^2 + b^2. find cosec x
Answers
Answered by
0
sin
n
x
+
1
sin
n
x
=
2
Solving
sin
x
+
1
sin
x
=
2
→
sin
2
x
−
2
sin
x
+
1
=
0
we have
sin
x
=
1
then
sin
n
x
+
1
sin
n
x
=
2
This can be also demonstrated by finite induction.
1) First it is true for
n
=
1
(with sin x = 1 of course)
2) Supposing that it is true for
n
then
3) Prove that it is true for
n
+
1
It is quite easy and it is left as an exercise.
n
x
+
1
sin
n
x
=
2
Solving
sin
x
+
1
sin
x
=
2
→
sin
2
x
−
2
sin
x
+
1
=
0
we have
sin
x
=
1
then
sin
n
x
+
1
sin
n
x
=
2
This can be also demonstrated by finite induction.
1) First it is true for
n
=
1
(with sin x = 1 of course)
2) Supposing that it is true for
n
then
3) Prove that it is true for
n
+
1
It is quite easy and it is left as an exercise.
Answered by
1
If (a^2 - b^2)sinx - 2abcosx = a^2 + b^2.......then find tanx & cosecx in terms of a & b. ... prove that (a^2 - b^2)\sin x - 2ab\cos x \le a^2 + b^2 and equality occurs when \tan ...
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