NIMCET 2013 — Mathematics PYQ

We are given the equation:

Step 1: Express $\sin x$ in terms of $\cos x$

From (Equation 1), we can rewrite it as:

Using the fundamental trigonometric identity ${\sin }^{2}x+{\cos }^{2}x=1$, we know that $1-{\sin }^{2}x={\cos }^{2}x$.

Therefore:

Step 2: Find the value of ${\cos }^{4}x$

To find ${\cos }^{4}x$, we square both sides of (Equation 2):

Step 3: Substitute into the required expression

We need to find the value of:

Using the relationships we found in (Equation 2) and (Equation 3):

• Substitute ${\cos }^{4}x$ with ${\sin }^{2}x$

• Substitute ${\cos }^{2}x$ with $\sin x$

The expression becomes:

Step 4: Final Evaluation

From the original given information in (Equation 1), we already know that:

Thus:

Final Answer: The value is $1$.