Advertisements
Advertisements
Question
Evaluate the following: `(2sin25° sin35° sec55° sec65°)/(5tan 29° tan45° tan61°) + (3cos20° cos50° cot70° cot40°)/(5tan20° tan50° sin70° sin40°)`
Advertisements
Solution
`(2sin25° sin35° sec55° sec65°)/(5tan 29° tan45° tan61°) + (3cos20° cos50° cot70° cot40°)/(5tan20° tan50° sin70° sin40°)`
= `(2sin(90° - 65°) sin(90° - 55°) sec55° sec65°)/(5tan(90° - 61°) xx 1 xx tan61°)`
= `(3cos(90° - 70°) cos(90° - 40°) cot(90° - 20°) cot(90° - 50°))/(5tan20° tan50° sin70° sin40°)`
= `(2cos65° cos55° xx 1/(cos55°) xx 1/(sec65°))/(5cot61° xx 1 xx 1/(cot61°)) + (3sin70° sin40° tan20° tan50°)/(5tan20° tan50° sin70° sin40°)`
= `(2)/(5) + (3)/(5)`
= `(5)/(5)`
= 1.
APPEARS IN
RELATED QUESTIONS
If sin x + cos y = 1 and x = 30°, find the value of y
If 4 cos2 x = 3 and x is an acute angle;
find the value of :
(i) x
(ii) cos2 x + cot2 x
(iii) cos 3x (iv) sin 2x
Solve the following equation for A, if 2 sin A = 1
Find the magnitude of angle A, if 2 cos2 A - 3 cos A + 1 = 0
If A = B = 60°, verify that: tan(A - B) = `(tan"A" - tan"B")/(1 + tan"A" tan"B"")`
In a trapezium ABCD, as shown, AB ‖ DC, AD = DC = BC = 24 cm and ∠A = 30°. Find: length of AB
Find the value 'x', if:
Evaluate the following: `(sec34°)/("cosec"56°)`
Express each of the following in terms of trigonometric ratios of angles between 0° and 45°: sin65° + cot59°
If A, B and C are interior angles of ΔABC, prove that sin`(("A" + "B")/2) = cos "C"/(2)`
