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Lesson Topics Discussion Quiz: Class Homework

Example1

Title: Trigonometry

Grade Lesson s5-p1

Explanation: The best way to understand SAT-4 is by looking at some examples. Take turns and read each example for easy understanding.

Examples

Topics → Definition Example1 Example2

Find the value of \$cos^-1 (x − y)\$ where y ranges from (0, 2π) and cos(x + y) = 1.

Step: 1

The given expression is simplify
⇒ cos(x + y) = 1
⇒ \$x + y = cos^-1(1)\$
⇒ x + y = 0°
⇒ y = 0° - x
⇒ x = 0° - y

Explanation:

Simplify the expression given, then determine the value of x.

Step: 2

Use the formula:
\$"sin"("x" - "y") = "sinx" "cosy" - "cosx" "siny"\$
\$"sin"("A" - "B") = "sinA" "cosB" - "cosA" "sinB"\$

Then plug the "x" value in the above formula and simplify the expression
⇒ \$"sin"(0° - "y") "cosy" - "cos"(0° - "y") "siny"\$
⇒ \$-"sin"("y") "cos"("y") - "cos"("y") "sin"("y")\$
⇒ \$-2"sin"("y") "cos"("y")\$
⇒ -sin2y

Explanation:

Apply the formula, substitute the value of x, and then simplify to obtain the expression as -sin2y.