If SecA = x + 1/4x , Then prove that SecA + TanA = 2x or 1/2x

-
If SecA = x + 1/4x , Then prove that SecA + TanA = 2x or 1/2x


SecA = x  +1/4x
∴, Sec²A = (x+1/4x)²
= x² + 2.x.1/4x + 1/16x²
= x² + 1/2 + 1/16x²


Now,
    Sec²A - Tan²A = 1
⇒ Tan²A = Sec²A - 1
⇒ Tan²A = x² + 1/2 + 1/16x² - 1
⇒ Tan²A = x² + 1/16x² - 1/2
⇒ Tan²A = x² - 2.x.1/4x + 1/16x²
⇒ Tan²A = (x-1/4x)²
⇒ TanA  = ± (x-1/4x)


∴
CASE 1:  TanA = x - 1/4x

 SecA + TanA 
= x + 1/4x + x -1/4x
= 2x

CASE 2: TanA = -(x - 1/4x)

 SecA + TanA
= x + 1/4x - (x - 1/4x)
=x + 1/4x - x + 1/4x
= 1/4x + 1/4x
= 2/4x
= 1/2x (Proved)

Comments

Post a Comment

Popular posts from this blog

A diwali cracker of mass 60 g, at rest, explodes into three pieces A, B and C of mass 10 g, 20 and 30 g respectively. After explosion velocities of A and B are 30 m/s along east and 20 m/s along north respectively. Find the instantaneous velocity of C.

-
Image
Q. A diwali cracker of mass 60 g, at rest, explodes into three pieces A, B and C of mass 10 g, 20 and 30 g respectively. After explosion velocities of A and B are 30 m/s along east and 20 m/s along north respectively. Find the instantaneous velocity of C. Ans:  
Read more

The measure of length and breadth of a rectangle are l = (30.0 ± 0.2) cm and b = (10.0 ± 0.1) cm. What is the percentage error in the calculation of area of rectangle?

-
The measure of length and breadth of a rectangle are l = (30.0 ± 0.2) cm and b = (10.0 ± 0.1) cm. What is the percentage error in the calculation of area of rectangle? Length =  30.0   ± 0.2 cm Breadth = 10.0 ± 0.1 cm Area  = Length  ×  Breadth   = (30.0 × 10.0) = 19.38 cm² ΔA = A × (ΔL/L + ΔB/B) = 300.00 × (0.2/30.0 + 0.1/10.0) = 5 cm² Area of rectangle = (300.00 ± 5.0) cm² percentage error in the calculation of area of rectangle =  ΔA/A  × 100  = 5/300  × 100  = 1.67%
Read more