Question

Value of theta , for sin 2 theta = 1, where theta <0<90° is:
(1) 30° (6) 60° (c) 45° (d) 135.​

Answer 1

Answer:

Right option is: (c) 45°

Step-by-step explanation:

The given condition is $sin2\theta$ = 1.

• We know the trigonometric formula: sin2$\theta$ = 2sin$\theta$cos$\theta$

                So, we can write 2sin$\theta$cos$\theta$ = 1

                                               sin$\theta$cos$\theta$ = $\frac{1}{2}$

• Calculation of $\theta$: As the value of $\theta$ is between 0° to 90°, so right answer will be among first three options. Lets verify them:

  (1) Putting $\theta$ = 30°, sin$\theta$ = sin30° = $\frac{1}{2}$ and cos$\theta$ = cos30° = $\frac{\sqrt{3} }{2}$

                                  sin$\theta$cos$\theta$ = sin30°cos30° = $\frac{\sqrt{3} }{4}$  

         Not satisfied the above condition, so $\theta$ ≠ 30°

(2) Putting $\theta$ = 60°, sin$\theta$ = sin60° = $\frac{\sqrt{3} }{2}$and cos$\theta$ = cos60° = $\frac{1}{2}$

                                  sin$\theta$cos$\theta$ = sin60°cos60° = $\frac{\sqrt{3} }{4}$  

         Not satisfied the above condition, so $\theta$ ≠ 60°

(3) Putting $\theta$ = 45°, sin$\theta$ = sin45° = $\frac{1}{\sqrt{2} }$ and cos$\theta$ = cos45° = $\frac{1}{\sqrt{2} }$

                                  sin$\theta$cos$\theta$ = sin45°cos45° = $\frac{1}{2}$  

         This value satisfies the above condition, so $\theta$ = 45°

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Answer 2

The correct answer is option C.

Given: The equation = Sin2Ф = 1.

To Find: The value of theta.

Solution:

As we know Sin90° = 1.

Sin2Ф = 1

Sin2Ф = Sin90°

2Ф = 90°

Ф = 45°

Hence, the value of theta is 45°.

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