Advertisements
Advertisements
Question
If sin θ = `3/4` show that `sqrt((cosec^2theta - cot^2theta)/(sec^2theta-1)) =sqrt(7)/3`
Solution
LHS = `sqrt((cosec^2theta - cot^2theta)/(sec^2 2-1))`
=` sqrt(1/tan^2theta)`
=`sqrt(cot^2theta)`
= `cottheta`
= `sqrt(cosec^2theta -1)`
= `sqrt(1/(3/4)^2-1)`
=`sqrt((4/3)^2-1)`
=`sqrt(16/9-1)`
=`sqrt((16-9)/9)`
=`sqrt(7/9)`
=`sqrt(7)/3`
= RHS
APPEARS IN
RELATED QUESTIONS
If A = B = 60°. Verify `tan (A - B) = (tan A - tan B)/(1 + tan tan B)`
If A = 30° and B = 60°, verify that cos (A + B) = cos A cos B − sin A sin B
If A and B are acute angles such that tan A = 1/2, tan B = 1/3 and tan (A + B) = `(tan A + tan B)/(1- tan A tan B)` A + B = ?
If tan θ = `1/sqrt(7) `show that ` (cosec ^2 θ - sec^2 θ)/(cosec^2 θ + sec^2 θ ) = 3/4`
In a ΔABC , ∠B = 90° , AB= 24 cm and BC = 7 cm find (i) sin A (ii) cos A (iii) sin C (iv) cos C
Evaluate:
cos600 cos300− sin600 sin300
If cosec θ = `sqrt5`, find the value of:
- 2 - sin2 θ - cos2 θ
- 2 + `1/sin^2"θ" – cos^2"θ"/sin^2"θ"`
In each of the following, one trigonometric ratio is given. Find the values of the other trigonometric.
sinB = `sqrt(3)/(2)`
In ΔABC, ∠B = 90°. If AB = 12units and BC = 5units, find: cos C
If sin A = `(7)/(25)`, find the value of : cot2A - cosec2A
