Trigonometry

The fundamental trigonometric identity states that sec²θ = 1 + tan²θ; rearranging gives sec²θ – tan²θ = 1, so answer B is correct. Choice A (0) is a common trap where students mistakenly think the two terms cancel, ignoring the constant 1 that remains after applying the identity.

Using the trigonometric identity for the sine of a sum, the expression simplifies directly to sine of 90 degrees, which equals 1. Option D is incorrect because 1/2 is merely the value of sine 30 degrees, which neglects the contribution of the second term in the addition.

Using the trigonometric identity for the sine of a sum, the expression simplifies directly to sine of 90 degrees, which equals 1. A diagram for this topic isn't available yet — the worked example below walks the same reasoning step by step.

• !Option D is incorrect because 1/2 is merely the value of sine 30 degrees, which neglects the contribution of the second term in the addition.
• !Option B is incorrect because 1/sqrt(2) represents the individual sine or cosine value, not their quotient.
• !Choice A (0) is a common trap where students mistakenly think the two terms cancel, ignoring the constant 1 that remains after applying the identity.

Answer each from memory — you'll see instantly whether you're right and why.

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