1+tansquare titha = ?
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1.) tan² θ + 1 = sec² θ to make it look identical to the right side as follows:
2.) (tan θ)² + 1 = sec² θ
Utilizing one of the basic trigonometric identities: tan θ = sin θ ∕ cos θ, we now substitute it into the left side of the above identity and simplify as follows:
3.) (sin θ ∕ cos θ)² + 1 = sec² θ
4.) (sin² θ ∕ cos² θ) + 1 = sec² θ
Now, combining the two terms on the left side by using the fact that the lowest common denominator = cos² θ and that 1 = cos² θ ∕ cos² θ, we have:
5.) (sin² θ ∕ cos² θ) + (cos² θ ∕ cos² θ) = sec² θ
6.) (sin² θ + cos² θ) ∕ cos² θ = sec² θ
Utililizing the basic identity: sin² θ + cos² θ =1 and substituting into the left side, we have:
7.) 1 ∕ cos² θ = sec² θ
8.) (1 ∕ cos θ)² = sec² θ
Since sec θ = 1 ∕ cos θ, we can substitute and simplify on the left side as follows:
9.) (sec θ)² = sec² θ
10.) sec² θ = sec² θ
HOPE THIS WILL HELP U
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