If tan $\theta =1$ and $\theta$ is acute find the value of sin $\theta + cos\theta$

Step 1: Determine the angle $\theta$

We are given that $\tan \theta = 1$ and $\theta$ is an acute angle. We know that the tangent of $45^\circ$ is $1$. Therefore, the angle $\theta$ must be $45^\circ$.

Step 2: Find the values of $\sin \theta$ and $\cos \theta$

Now that we know $\theta = 45^\circ$, we can find the values of $\sin 45^\circ$ and $\cos 45^\circ$. Both $\sin 45^\circ$ and $\cos 45^\circ$ are equal to $\frac{1}{\sqrt{2}}$.

Step 3: Calculate $\sin \theta + \cos \theta$

Finally, we substitute the values of $\sin 45^\circ$ and $\cos 45^\circ$ into the expression $\sin \theta + \cos \theta$. We add the two fractions and then rationalize the denominator to simplify the expression.

More from this chapter

• **EXERCISE 8.3** **1.** Express the trigonometric ratios sin A, tan A and sec A in terms of cot A.
• Cos A / 1 + sin a + 1 + sin a / cos A is equal to 2 sec a
• write all the other trigonometric ratios of angle A in terms of sec A
• Express all the trigonometric ratios in terms of Sin A
• Express the trigonometric ratio sign a sec a tan a in terms of cot a
• Prove that √(sec² A + csc² A) = tan A + cot A
• (secθ - tanθ) = (1)/(m) --- (2) Adding (1) & (2) secθ + tanθ + secθ - tanθ = (1)/(m) + (m)/(1) 2secθ = (1 + m²)/(m) secθ = (1 + m²)/(2m) (Hence proved) 2) If as
• If tanθ + secθ = m, prove that secθ = (m² + 1)/(2m).

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