Home
Class 12
MATHS
If a,b,c inR then prove that sec^2theta=...

If `a,b,c inR` then prove that `sec^2theta=(bc+ca+ab)/(a^2+b^2+c^2)`only if a = b = c.

Text Solution

Verified by Experts

We know that `sec^2thetage1`
`:. (bc+ca+ab)/(a^2+b^2+c^2)ge 1`
`rArr bc+ca+abgea^2+b^2+c^2`
`rArra^2+b^2+c^2-ab-bc-cale0`
`rArr(a-b)^2+(b-c)^2+(c-a)^2le0`
`rArra-b=0,b-c=0" and "c-a=0`
`rArra=b=c`
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise Concept Application Exercises 2.6|1 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise Concept Application Exercises 2.7|1 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise Concept Application Exercises 2.4|4 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE PUBLICATION|Exercise Archives (Numerical value type)|4 Videos

  • TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|2 Videos

Similar Questions

Explore conceptually related problems

If a^2+b^2+c^2-ab-bc-ca=0 then, prove that a=b=c

if a:b = b:c prove that ((a+b)/(b+c))^2 = (a^2+b^2)/(b^2+c^2) .

If (a-b), (b-c), (c-a) are in GP then prove that (a+b+c)^2 =3(ab+bc+ca)..

If a+b+c= 0 prove that 1/(2a^2+bc)+1/(2b^2+ca)+1/(2c^2+ab)=0

If a, b, c are all positive, prove that 6abc le bc(b + c) + ca(c + a) + ab(a + b)

In the right-angled triangle ABC, /_C = 90^(@) .If the length of perpendicular drawn from C on AB be p and AB=c,BC =a,CA=b , then prove that (a)(1)/(p^(2))=(1)/(a^(2) )+ (1)/(b^(2)) , (b) pc = ab .

Find the product (2a + b+c) (4a ^(2) + b ^(2) + c ^(2) - 2ab -bc -2ca)

If a, b and c are three positive real numbers, show that a^2 + b^2 + c^2 ge ab + bc + ca

If a/b = b/c = c/d , then prove that (a^(2) + b^(2) + c^(2))(b^(2) + c^(2)+d^(2)) = (ab + bc cd)^(2)

If a : b = b : c , then prove that (abc(a+b+c)^(3))/((ab+bc+ca)^(3)) = 1