Grade 10Trigonometry
TanA+sinA=m and tanA_sinA=n show that (m^2-n^2)=16mn
TanA+sinA=m and tanA_sinA=n show that (m^2-n^2)=16mn
2 Answers
Arun
m = tanA + sinA
n = tanA - sinA
L.H.S. = {(tanA + sinA)² - (tanA-sinA)²}
{tan²A + sin²A + 2tanAsinA - (tan²A + sin²A - 2tanAsinA)}²
⇒ = (4tanAsinA)²
16tan²Asin²A
16tan²A(1 - cos²A)
16tan²A - tan²Acos²A
16tan²A - sin²A/cos²A × cos²A
16tan²A - sin²A
16(tan²A + sin²A) (tan²A - sin²A)
= 16 mn
n = tanA - sinA
L.H.S. = {(tanA + sinA)² - (tanA-sinA)²}
{tan²A + sin²A + 2tanAsinA - (tan²A + sin²A - 2tanAsinA)}²
⇒ = (4tanAsinA)²
16tan²Asin²A
16tan²A(1 - cos²A)
16tan²A - tan²Acos²A
16tan²A - sin²A/cos²A × cos²A
16tan²A - sin²A
16(tan²A + sin²A) (tan²A - sin²A)
= 16 mn
Deepak Kumar Shringi
Other Related Questions on trigonometry
In ABC, if cot A+cot B+cot C = cosecA cosecB cosecC, then prove that ABC is right angle triangle.
In ABC, if cot A+cot B+cot C = cosecA cosecB cosecC, then prove that ABC is right angle triangle.
trigonometry
Last Activity: 3 Years ago
- Find the general solution of equation tan3∂=cot2∂
For all angles between -720 and +720
- Find the general solution of equation tan3∂=cot2∂
For all angles between -720 and +720
trigonometry
Last Activity: 4 Years ago
Derive a formula for the area of the triangle, given b, A, B, and C. That is, derive the formula: (b^2sinAsinC)/(2sinB)
Derive a formula for the area of the triangle, given b, A, B, and C. That is, derive the formula: (b^2sinAsinC)/(2sinB)
trigonometry
Last Activity: 4 Years ago
WHAT IS THE LIMIT WHEN X TOWARDS TO 0 OF sin6x/5x ? lim𝑥→0 𝑠𝑖𝑛6𝑥/5𝑥
WHAT IS THE LIMIT WHEN X TOWARDS TO 0 OF sin6x/5x ? lim𝑥→0 𝑠𝑖𝑛6𝑥/5𝑥
trigonometry
Last Activity: 4 Years ago