(ii)
I am a beginner in logarithms, so i couldn't get this part.
Now its clear.
thanks.
]]>Post 12 shows what this problem is asking.
exp is an alternative notation for e to the power of ....
And lnx is the inverse function to exp.
The quadratic has two solutions: 1 and 27.
The sine series is geometric with first term sin squared and common ratio also sin squared.
As sin squared is less than 1, you can use the sum to infinity formula to sum this.
So either
(i)
ln 1 is the power you have to raise e to, in order to get 1. ie. zero.
=> theta = zero but we are told theta is > 0, so this leads to no solutions for theta.
(ii)
so
and
This can be 'rationalised' to
Bob
]]>exp. means:-
e^{(sin^2x+sin^4x+sin^6x+......+∞)log_e3}
using GP, the sum of (sin^2x+sin^4x+sin^6x+......+∞) comes to be tan^2x
now if we get the value of tan^2x , we can easily get the required value.
Now how to get the value of tan^2x?
and what does In(x) means??
ln(x) is a notation often used in place of log base e.
]]>e^{(sin^2x+sin^4x+sin^6x+......+∞)log_e3}
using GP, the sum of (sin^2x+sin^4x+sin^6x+......+∞) comes to be tan^2x
now if we get the value of tan^2x , we can easily get the required value.
Now how to get the value of tan^2x?
and what does In(x) means??
]]>niharika_kumar wrote:If exp.
satisfies the equationDoes it mean:
If
then???
What is exp.?
The way the question seems too be worded, one would presume the OP wants to find a θ such that:
andThe sum is trivial (a geometric series), and the quadratic also factorises nicely -- then, you just need to re-write cosθ / (sinθ + cosθ) in terms of tanθ, and you're done.
]]>]]>
If exp.
satisfies the equation
Does it mean:
If
then???
What is exp.?
]]>Is that a Class XI level problem?
]]>