To Prove: Dividing the numerator and denominator by cosθ, we get,Now, we know that, sec2θ - tan2θ = 1Therefore, replacing 1 by sec2θ - tan2θ in the numerator only, we get,As we know,a2 - b2 = (a-b)(a+b)= secθ + tanθNow, multiplying and dividing by secθ - tanθ, we get,As we know,sec2θ - tan2θ = 1= R.H.SHence, proved.

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Q. 47 B4.1( 47 Votes )

Prove the followi

Class 10th RD Sharma - Mathematics 6. Trigonometric Identities

Answer :

To Prove:

Dividing the numerator and denominator by cosθ, we get,

Now, we know that,
sec²θ - tan²θ = 1
Therefore, replacing 1 by sec²θ - tan²θ in the numerator only, we get,

As we know,
a² - b² = (a-b)(a+b)

= secθ + tanθ
Now, multiplying and dividing by secθ - tanθ, we get,

As we know,
sec²θ - tan²θ = 1

= R.H.S
Hence, proved.