Let -pi/6 < theta < -pi/12. Suppose alph...

Let `-pi/6 < theta < -pi/12`. Suppose `alpha_1 and beta_1`, are the roots of the equation `x^2-2xsectheta + 1=0` and `alpha_2 and beta_2` are the roots of the equation `x^2 + 2xtantheta-1=0`. If `alpha_1 > beta_1` and `alpha_2 >beta_2`, then `alpha_1 + beta_2` equals:

`2(sec theta-tan theta)`

`2 sec theta`

`-2 tan theta`

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

TRIGONOMETRIC FUNCTIONS AND IDENTITIES
ARIHANT MATHS|Exercise Exercise (Subjective Type Questions)|22 Videos
TRIGONOMETRIC EQUATIONS AND INEQUATIONS
ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|12 Videos
VECTOR ALGEBRA
ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|9 Videos

Similar Questions

Explore conceptually related problems

If "cot"(alpha+beta=0, then "sin"(alpha+2beta can be

If a tan alpha+b tan beta=(a+b) tan ((alpha+beta)/2) , where alpha ne beta , prove that : a cos beta= b cos alpha .

If sin (alpha+beta)=1, sin (alpha-beta)=1/2 , then tan (alpha+ 2beta). tan (2 alpha+beta) is equal to :

If cos^-1 alpha + cos^-1 beta + cos^-1 gamma = 3 pi , then alpha(beta + gamma) + beta (gamma + alpha) + gamma (alpha + beta) equals

If tan(2alpha+beta)=x & tan(alpha+2beta)=y , then [ tan3(alpha+beta)]. [ tan(alpha-beta)] is equal to (wherever defined)

If alpha+beta=pi/2a n dbeta+gamma=alpha, then tanalpha equals

The lengths of the sides of a triangle are alpha-beta, alpha+beta and sqrt(3alpha^2+beta^2), (alpha>beta>0) . Its largest angle is

f: D->R, f(x) = (x^2 +bx+c)/(x^2+b_1 x+c_1) where alpha,beta are the roots of the equation x^2+bx+c=0 and alpha_1,beta_1 are the roots of x^2+b_1 x+ c_1= 0 . Now answer the following questions for f(x). A combination of graphical and analytical approach may be helpful in solving these problems. (If alpha_1 and beta_1 are real, then f(x) has vertical asymptote at x = (alpha_1,beta_1) If alpha_1 lt alpha lt beta_1 lt beta , then

If alpha_(1), alpha_(2), alpha_(3), beta_(1), beta_(2), beta_(3) are the values of n for which sum_(r=0)^(n-1)x^(2r) is divisible by sum_(r=0)^(n-1)x^(r ) , then the triangle having vertices (alpha_(1), beta_(1)),(alpha_(2),beta_(2)) and (alpha_(3), beta_(3)) cannot be

int _(alpha)^(beta) 2x dx is equal to

ARIHANT MATHS-TRIGONOMETRIC FUNCTIONS AND IDENTITIES-Exercise (Questions Asked In Previous 13 Years Exam)

Let alpha and beta be non-zero real numbers such that 2 ( cos beta -...
Text Solution
|
Let -pi/6 < theta < -pi/12. Suppose alpha1 and beta1, are the roots of...
Text Solution
|
The value of overset(13)underset(k=1)(sum) (1)/(sin((pi)/(4) + ((k-1)p...
Text Solution
|
Let f:(-1,1)vecR be such that f(cos4theta)=2/(2-sec^2theta) for theta ...
Text Solution
|
The number of all possible values of theta, where 0 lt theta lt pi, fo...
Text Solution
|
For 0 lt theta lt pi/2 , the solution (s) of sum(m=1)^6cos e c(theta+(...
Text Solution
|
If sin^ 4 x/2+cos^4 x/3 =1/5 then
Text Solution
|
Let theta in (0, pi/4) and t(1)=tan theta)^(tan theta), t(2)=(tan thet...
Text Solution
|
if cos(alpha-beta)=1a n dcos(alpha+beta)=l/e , where alpha,betamu in [...
Text Solution
|
If 5 (tan ^(2) x - cos ^(2) x ) = 2 cos 2x +9, then the value of cos 4...
Text Solution
|
Let F(k)(x)=1/k (sin^(k)x+cos^(k)x), where x in R and k ge 1, then fin...
Text Solution
|
The expression (tanA)/(1-cotA)+(cotA)/(1-tanA) can be written as (1) s...
Text Solution
|
If a Delta PQR " if" 3 sin P + 4 cos Q = 6 and 4 sin Q + 3 cos P =1 , ...
Text Solution
|
If A = sin^2x + cos^4 x, then for all real x :
Text Solution
|
Let cos(alpha+beta)""=4/5 and let sin (alpha+beta)""=5/(13) where 0lt=...
Text Solution
|
If cosalpha+cosbeta+cosgamma=0=sinalpha+sinbeta+singamma, then which...
Text Solution
|
A triangular park is enclosed on two sides by a fence and on the third...
Text Solution
|
In Delta PQR , /R=pi/4, tan(P/3), tan(Q/3) are the roots of the equati...
Text Solution
|