Question

please prove that all the question. ​

Answer 1

Answer:

15) let theta=x.

given,

((secx-tan x)^2+1)/(sec x.cosec x-tan x. cosec x)

(a-b)^2=a^2-2ab+b^2

LHS:

=(sec^2x-2sec x. tan x+tan^2 x+1)

/sec x. cosec x- (sin x/cos x)

(1/sin x)

=(sec^2 x-2sec x. tan x+sec^2 x)/

sec x. cosec x-(1/cos x)

=(2sec^2 x -2 sec x. tanx)/ (sec x

cosec x-sec x)

=2sec x(sec x- tan x)/sec x

(cosec x-1)

=2((1/cos x)-(sin x/cos x))/sec x

((1/sin x)-1)

=2((1-sinx)/cosx)/(1-sinx)/sinx

=2((1-sinx).sinx)/(1-sinx).cosx

=2sinx/cosx

=2 tanx

LHS=RHS

Hence proved

Answer 2

Answer:

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