Asked by Anonymous
                this question confused me can you please show me how its done.
Reduce (csc^2 x - sec^2 X) to an expression containing only tan x.
            
        Reduce (csc^2 x - sec^2 X) to an expression containing only tan x.
Answers
                    Answered by
            MathMate
            
    Try using the following identities:
1 + tan²(x) = sec²(x)
1 + cot²(x) = csc²(x)
tan(x) = 1/cot(x)
    
1 + tan²(x) = sec²(x)
1 + cot²(x) = csc²(x)
tan(x) = 1/cot(x)
                    Answered by
            Anonymous
            
    csc x = 1/sin x
sec x = 1/cos x
tan x = 1/cot x
sin^2 x + cos^2 x = 1
1 + cot^2 x = csc^2 x
tan^2 x + 1 = sec^2 x
csc^2 x - sec^2 x
= 1 + cot^2 x - (1 + tan^2 x)
= cot^2 x - tan^2 x
= (1/tan^2 x) - tan^2 x
    
sec x = 1/cos x
tan x = 1/cot x
sin^2 x + cos^2 x = 1
1 + cot^2 x = csc^2 x
tan^2 x + 1 = sec^2 x
csc^2 x - sec^2 x
= 1 + cot^2 x - (1 + tan^2 x)
= cot^2 x - tan^2 x
= (1/tan^2 x) - tan^2 x
                    Answered by
            Anonymous
            
    Is it correct??
    
                    Answered by
            MathMate
            
    Correct!
    
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