Saved Bookmarks
| 1. |
If sin θ + sin² θ = 1 , prove that cos² θ + cos⁴ θ = 1 |
|
Answer» ANSWER :- ______________________ • Given :- sinθ + sin²θ = 1 • To find :- The value of : cos²θ + cos⁴θ • SALUTATION :- sinθ + sin²θ = 1 sinθ = 1 - sin²θ sinθ = cos²θ ---------- ( i ) [ • As sin²θ + cos²θ = 1 So , sin²θ = 1 - cos²θ ] ★ Method - 1 sinθ = cos²θ ( sinθ )² = ( cos²θ )² sin²θ = cos⁴θ 1 - cos²θ = cos⁴θ cos⁴θ + cos²θ = 1 [ ★ Required answer ] __________________ ★ Method - 2 cos²θ + cos⁴θ = sinθ + ( sinθ )² [ • Putting the value of cos²θ = sinθ ] = sinθ + sin²θ = 1 [ • Given , sinθ + sin²θ = 1 ] • So FINALLY , [ cos²θ + cos⁴θ = 1 ] ______________________________ ★ Be BRAINLY ★ |
|