Simplify the expression: cos³θ + sin³θcos θ + sin θ + cos³θ − sin³θcos θ − sin θ.
व्यंजक (Expression) को सरल कीजिए: cos³θ + sin³θcos θ + sin θ + cos³θ − sin³θcos θ − sin θ
Answer और ExplanationAnswer and explanation
Answer: (C) 2
a³ + b³ = (a + b)(a² − ab + b²) और a³ − b³ = (a − b)(a² + ab + b²)
पहला भाग = cos²θ − cos θ sin θ + sin²θ = 1 − sin θ cos θ
दूसरा भाग = cos²θ + cos θ sin θ + sin²θ = 1 + sin θ cos θ
योग = (1 − sin θ cos θ) + (1 + sin θ cos θ) = 2
✓
उत्तर 2 है।
a³ + b³ = (a + b)(a² − ab + b²) and a³ − b³ = (a − b)(a² + ab + b²)
First part = cos²θ − cos θ sin θ + sin²θ = 1 − sin θ cos θ
Second part = cos²θ + cos θ sin θ + sin²θ = 1 + sin θ cos θ
Sum = (1 − sin θ cos θ) + (1 + sin θ cos θ) = 2
✓
The answer is 2.
SMART APPROACH
θ = 0° रखें: 1 + 01 + 0 + 1 − 01 − 0 = 2।
Put θ = 0°: 1 + 01 + 0 + 1 − 01 − 0 = 2.
Source: Selection Post Phase XIV (Graduate) · 24 Sep 2026 · Shift 1। Solution: Prashant Sir, Vijayastra।Source: Selection Post Phase XIV (Graduate) · 24 Sep 2026 · Shift 1. Solution by Prashant Sir, from Vijayastra.