SSC संयुक्त स्नातक स्तरीय टीयर-1 प्रैक्टिस सेट 1

Question : 70 of 100

Marks: +1, -0

[(\sec ^{3} x-\tan ^{3} x) \/(\sec x-\tan x)]

-2 \tan ^{2} x-\sec x \tan x

सरलीकृत मान क्या है?

Solution:

(\sec ^{3} x-\tan ^{3} x) /(\sec x-\tan x)

-2 \tan ^{2} x-\sec x \tan x

={(\sec x-\tan x)(\sec ^{2} x+\tan ^{2} x +\sec x \tan x)}/(\sec x-\tan x)

-2 \tan ^{2} x-\sec x \tan x

=\sec ^{2} x+\tan ^{2} x+\sec x \tan x

-2 \tan ^{2} x-\sec x \tan x

=\sec ^{2} x+\tan ^{2} x-2 \tan ^{2} x

=\sec ^{2} x-\tan ^{2} x=1

Go to Question:

Prev Question

Next Question