If p sin A − cos A = 1, then p2 − (1 + p2) cos A equals:
1
Solution: Using Substitution
Step 1: Choose a convenient angle for A
The core idea of this method is to choose a value for angle A that simplifies the trigonometric functions (sin A and cos A). A perfect choice is A = 90°, because sin(90°) = 1 and cos(90°) = 0, which are easy numbers to work with.
Step 2: Solve for 'p' using the chosen angle
Substitute A = 90° into the given equation:
p sin(90°) − cos(90°) = 1
Since sin(90°) = 1 and cos(90°) = 0, the equation becomes:
p(1) − 0 = 1
This simplifies directly to:
p = 1
Step 3: Evaluate the target expression
Now we substitute the values we have (A = 90°, cos(90°) = 0, and p = 1) into the expression we need to find:
p² − (1 + p²) cos A
Plugging in the values:
(1)² − (1 + (1)²) cos(90°)
Simplify the terms inside the parentheses:
1 − (1 + 1) × 0 1 − (2) × 0
Any number multiplied by zero is zero:
1 − 0
Result = 1
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