If sec x + cos x = 3, then $$tan^{2}x - sin^{2}x$$ is
Expression : $$sec x + cos x = 3$$
Squaring both sides, we get :
=> $$sec^2 x + cos^2 x + 2.sec x . cos x = 9$$
=> $$sec^2 x + cos^2 x = 9-2 = 7$$
To find : $$tan^{2}x - sin^{2}x$$
= $$sec^2 x - 1 - (1 - cos^2 x)$$
= $$sec^2 x + cos^2 x - 2 = 7-2 = 5$$
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