L.H.S = cotx + tan x
= cotx +tan x * (cot x / cot x)
= cot x * { 1 + tanx * (1 / cot x)}
but (1 / cot x) = tan x
= cot x * {1 + tanx * tan x}
= cot x * {1 + tan^2 x }
but (1 + tan^2 x) = sec^2 x
then
L.H.S = cot x * sec^2 x
L.H.S = R.H.S
THANK YOU.
cotx = cosx/sinx
tanx = sinx/cosx
cosx/sinx + sinx/cosx = cotx sec2x?
[cos^2 x + sin^2 x]/sinx cosx = cotx sec2x?
But: cos^2 x + sin^2 x = 1
1/sinx cosx = cotx sec2x?
cscx secx = cotx sec 2x?
not = cotx sec 2x
consider the lhs
cotx+tanx= 1/tanx+tanx=1+tan^2x/tanx ( on taking lcm tanx)
sec^2x/tanx ( since sec^2x-tan^2x=1)
cotxsec^2x=rhs
[since 1/tanx=cotx]
[in your question it is sec^2x not sec2x check with it]
Copyright © 2024 ANSWERS.MX - All rights reserved.
Answers & Comments
Verified answer
L.H.S = cotx + tan x
= cotx +tan x * (cot x / cot x)
= cot x * { 1 + tanx * (1 / cot x)}
but (1 / cot x) = tan x
= cot x * {1 + tanx * tan x}
= cot x * {1 + tan^2 x }
but (1 + tan^2 x) = sec^2 x
then
L.H.S = cot x * sec^2 x
L.H.S = R.H.S
THANK YOU.
cotx = cosx/sinx
tanx = sinx/cosx
cosx/sinx + sinx/cosx = cotx sec2x?
[cos^2 x + sin^2 x]/sinx cosx = cotx sec2x?
But: cos^2 x + sin^2 x = 1
1/sinx cosx = cotx sec2x?
cscx secx = cotx sec 2x?
not = cotx sec 2x
consider the lhs
cotx+tanx= 1/tanx+tanx=1+tan^2x/tanx ( on taking lcm tanx)
sec^2x/tanx ( since sec^2x-tan^2x=1)
cotxsec^2x=rhs
[since 1/tanx=cotx]
[in your question it is sec^2x not sec2x check with it]