Question

if Sinθ + Cosθ = a, then what is the value of (Secθ - Cosecθ) = _______?​

Answer 1

Answer:

L.H.S.

=(sinθ+secθ)²+(cosθ+cosecθ)²

=sin²θ+2sinθsecθ+sec²θ+cos²θ+2cosθcosecθ+cosec²θ

=sin²θ+cos²θ+2(sinθsecθ+cosθcosecθ)+sec²θ+cosec²θ

=1+2(sinθ/cosθ+cosθ/sinθ)+(1/cos²θ+1/sin²θ)

=1+2(sin²θ+cos²θ)/sinθcosθ+(sin²θ+cos²θ)/sin²θcos²θ

=1+2/sinθcosθ+1/sin²θcos²θ

=1+2secθcosecθ+sec²θcosec²θ

R.H.S.

=(1+secθcosecθ)²

=1²+2×1×(secθcosecθ)+(secθcosecθ)²

=1+2secθcosecθ+sec²θcosec²θ

∴, L.H.S.=R.H.S. (Proved)

Answer 2

Answer:

Answer

Let's consider the side of the plot as 3x, 5x and 7x.

So the sum of all these sides would be 300 m.

Now we need to do this equation to find the value of 'x' ⇒ 3x+5x+7x=3003x+5x+7x=300

Let's solve your equation step-by-step

3x+5x+7x=3003x+5x+7x=300

Step 1: Simplify both sides of the equation.

3x+5x+7x=3003x+5x+7x=300

(Combine Like Terms)

(3x+5x+7x)=300(3x+5x+7x)=300

15x=30015x=300

Step 2: Divide both sides by 15.

\frac{15x}{15} =\frac{300}{15}

15

15x

=

15

300

x= 20x=20

Now the sides of the triangle would be ⇒

Side A ⇒ 3×20 = 60 m

Side B ⇒ 5×20 = 100 m

Side C ⇒ 7×20 = 140 m

According to Heron Law we find area with this formula ⇒ \sqrt{s(s-a)(s-b)(s-c)}

s(s−a)(s−b)(s−c)

Over here 's' is the half of the perimeter which is 300 here. So the value of p would be 150.

\sqrt{150(150-60)(150-100)(150-140)}

150(150−60)(150−100)(150−140)

\sqrt{150(90)(50)(10)}

150(90)(50)(10)

\sqrt{150(45000)}

150(45000)

\sqrt{6750000}

6750000

1500\sqrt{3}m^{3}1500

3

m

3

∴ The area would be 1500√3m³.

\rule{300}{1}