हिंदी

If sec A = cosec A and 0° ∠A ∠90°, state the value of A - Mathematics

Advertisements
Advertisements

प्रश्न

If sec A = cosec A and 0° ∠A ∠90°, state the value of A

योग

उत्तर

sec A = cosec A
cos A = sin A
cos2A = sin2A
cos2 A = 1 – cos2A
2cos2A = 1

cos A = `(1)/(sqrt2)`
A = 45°

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 23: Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios] - Exercise 23 (A) [पृष्ठ २९१]

APPEARS IN

सेलिना Concise Mathematics [English] Class 9 ICSE
अध्याय 23 Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Exercise 23 (A) | Q 7.2 | पृष्ठ २९१

संबंधित प्रश्न

Find the value of x in the following :

tan 3x = sin 45º cos 45º + sin 30º


Evaluate the following in the simplest form: sin 60º cos 45º + cos 60º sin 45º


`(1- tan^2 45°)/(1+tan^2 45°)` = ______


Show that tan 48° tan 23° tan 42° tan 67° = 1


Evaluate the following :

`((sin 27^@)/(cos 63^@))^2 - (cos 63^@/sin 27^@)^2`


Express each one of the following in terms of trigonometric ratios of angles lying between 0° and 45°

 sin 67° + cos 75°


Prove that `sin 70^@/cos 20^@  + (cosec 20^@)/sec 70^@  -  2 cos 20^@ cosec 20^@ = 0`


Prove the following :

`(cos(90^@ - theta) sec(90^@ - theta)tan theta)/(cosec(90^@ - theta) sin(90^@ - theta) cot (90^@ -  theta)) + tan (90^@ - theta)/cot theta = 2`


Prove the following

 sin (50° − θ) − cos (40° − θ) + tan 1° tan 10° tan 20° tan 70° tan 80° tan 89° = 1


Evaluate: `4(sin^2 30 + cos^4 60^@) - 2/3 3[(sqrt(3/2))^2 . [1/sqrt2]^2] + 1/4 (sqrt3)^2`


Evaluate: `(2sin 68)/cos 22 - (2 cot 15^@)/(5 tan 75^@) - (8 tan 45^@ tan 20^@ tan 40^@ tan 50^@ tan 70^@)/5`


Evaluate: `(3 cos 55^@)/(7 sin 35^@) -  (4(cos 70 cosec 20^@))/(7(tan 5^@ tan 25^@ tan 45^@ tan 65^@ tan  85^@))`


Prove that

sin (70° + θ) − cos (20° − θ) = 0


Prove that:

sin 60° cos 30° + cos 60° . sin 30°  = 1


find the value of: cosec2 60° - tan2 30°


find the value of: sin2 30° + cos2 30°+ cot2 45°


Prove that:

4 (sin4 30° + cos4 60°) -3 (cos2 45° - sin2 90°) = 2


If sin x = cos y; write the relation between x and y, if both the angles x and y are acute.


Evaluate : 

`(3 sin 3"B" + 2 cos(2"B" + 5°))/(2 cos 3"B" – sin (2"B" – 10°)` ; when "B" = 20°.


If A = B = 45° ,
show that:
cos (A + B) = cos A cos B - sin A sin B


If A = 30°;
show that:
(sinA - cosA)2 = 1 - sin2A


Without using tables, evaluate the following sec45° sin45° - sin30° sec60°.


Without using tables, evaluate the following: tan230° + tan260° + tan245°


Find the value of x in the following: cos2x = cos60° cos30° + sin60° sin30°


If sinθ = cosθ and 0° < θ<90°, find the value of 'θ'.


Without using table, find the value of the following: `(tan^2 60° + 4cos^2 45° + 3sec^2 30° + 5cos90°)/(cosec30° + sec60° - cot^2 30°)`


If sin(A - B) = sinA cosB - cosA sinB and cos(A - B) = cosA cosB + sinA sinB, find the values of sin15° and cos15°.


If sin(A - B) = `(1)/(2)` and cos(A + B) = `(1)/(2)`, find A and B.


Find the value of the following:

(sin 90° + cos 60° + cos 45°) × (sin 30° + cos 0° – cos 45°)


Prove the following:

`(sqrt(3) + 1) (3 - cot 30^circ)` = tan3 60° – 2 sin 60°


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×