if sinx=cosx
Then cosecx=????
well, where does sinx = cosx?
Divide by cosx, and you have
tanx = 1
Look familiar?
Secx
To solve this equation, we need to use trigonometric identities and formulas.
Given: sinx = cosx
We know that cosec(x) is the reciprocal of sin(x). Therefore, we need to find the reciprocal of both sides of the equation sinx = cosx.
Reciprocal of sinx:
cosecx = 1/sinx
Now, let's substitute the value of sinx from the given equation sinx = cosx:
cosecx = 1/(cosx)
But we need to manipulate it to have its reciprocal in the numerator, as it is more common and easier to work with.
To do this, we will multiply both the numerator and denominator by cosx:
cosecx = (1 * cosx) / (cosx * cosx)
Simplifying further:
cosecx = cosx / (cosx * cosx)
Finally, simplifying the denominator:
cosecx = cosx / cos^2(x)
So, when sinx = cosx, the value of cosecx is cosx / cos^2(x).