Question

The value of sin(450 + α) – cos (450 – α) is

Select one:--:--:
a. 2sinα
b. 0
c. 1
d. 2cosα​

Answer 1

$\textbf{To find:}$

$\textsf{The value of}\;\mathsf{sin(450^\circ+\alpha)-cos(450^\circ-\alpha)}$

$\textbf{Solution:}$

$\mathsf{Consider,}$

$\mathsf{sin(450^\circ+\alpha)-cos(450^\circ-\alpha)}$

$\mathsf{Using,}$

$\boxed{\mathsf{sin(A+B)=sinA\,cosB+cosA\,sinB}}$

$\boxed{\mathsf{cos(A-B)=cosA\,cosB+sinA\,sinB}}$

$\mathsf{=[sin450^\circ\,cos\alpha+cos450^\circ\,sin\alpha]-[cos450^\circ\,cos\alpha+sin450^\circ\,sin\alpha]}$

$\mathsf{=[sin(360^\circ+90^\circ)\,cos\alpha+cos(360^\circ+90^\circ)\,sin\alpha]-[cos(360^\circ+90^\circ)\,cos\alpha+sin(360^\circ+90^\circ)\,sin\alpha]}$

$\mathsf{=[sin90^\circ\,cos\alpha+cos90^\circ\,sin\alpha]-[cos90^\circ\,cos\alpha+sin90^\circ\,sin\alpha]}$

$\mathsf{=[(1)\,cos\alpha+(0)\,sin\alpha]-[(0)\,cos\alpha+(1)\,sin\alpha]}$

$\mathsf{=(cos\alpha+0)-(0+sin\alpha)}$

$\mathsf{=cos\alpha-sin\alpha}$

$\implies\boxed{\mathsf{sin(450^\circ+\alpha)-cos(450^\circ-\alpha)=cos\alpha-sin\alpha}}$

Answer 2

Answer:

Given : Perimeter = 440 m

Let the length of rectangular field = lx and breadth = 4x

2(l + b) = Perimeter

2(7x + 4x) = 440 m

2(11x) = 440 m

22x = 440 m

x = 440/22

x = 11 m

∴ Length = 7x = 7 x 11 = 77 m

Breadth = Ax = 4 x 11 = 44 m

Cost of fencing per m = ₹150

Cost of fencing 440 m = ₹150 x 440 = ₹66,000

Step-by-step explanation: