Question:
If \(\sin\theta + \sin^2\theta = 1\), then find the value of \(\cos^2\theta + \cos^4\theta\).
यदि \(\sin\theta + \sin^2\theta = 1\) है, तो \(\cos^2\theta + \cos^4\theta\) का मान ज्ञात कीजिए।
Options:
- 0
- 1
- 2
- −1
- 0
- 1
- 2
- −1
Correct Answer: b)
Explanation:
Given \(\sin\theta + \sin^2\theta = 1 \implies \sin\theta = 1 – \sin^2\theta = \cos^2\theta\).
Squaring both sides: \(\sin^2\theta = \cos^4\theta\).
Now, \(\cos^2\theta + \cos^4\theta = \sin\theta + \sin^2\theta = 1\).
दिया है: \(\sin\theta + \sin^2\theta = 1 \implies \sin\theta = 1 – \sin^2\theta = \cos^2\theta\)।
दोनों पक्षों का वर्ग करने पर: \(\sin^2\theta = \cos^4\theta\)।
अतः, \(\cos^2\theta + \cos^4\theta = \sin\theta + \sin^2\theta = 1\)।