मराठी

Prove That: Sin θ Cos (90° - θ ) + Sin (90° - θ) Cos θ = 1 - Mathematics

Advertisements
Advertisements

प्रश्न

Prove that:

sin θ cos (90° - θ ) + sin (90° - θ) cos θ = 1

बेरीज

उत्तर

LHS = sin θ cos (90° - θ) + sin (90° - θ) cosθ

= sin θ sin θ + cos θ cos θ

= sin2 θ + cos2 θ 

= 1 

= RHS

Hence proved.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 7: Trigonometric Ratios of Complementary Angles - Exercises [पृष्ठ ३१३]

APPEARS IN

आर एस अग्रवाल Mathematics [English] Class 10
पाठ 7 Trigonometric Ratios of Complementary Angles
Exercises | Q 5.1 | पृष्ठ ३१३

व्हिडिओ ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्‍न

Without using trigonometric tables, evaluate 

`sin^2 34^@ + sin^2 56^@ + 2tan 18^@ tan 72^@ - cot^2 30^@`


Without using trigonometric tables, evaluate :
`sin 16^circ/cos 74^circ`


Without using trigonometric tables, evaluate :

`cot 38^circ/tan 52^circ`


Without using trigonometric tables, prove that:

tan 71° − cot 19° = 0


Without using trigonometric tables, prove that:

cosec 80° − sec 10° = 0


Without using trigonometric tables, prove that:

tan48° tan23° tan42° tan67° = 1


Prove that:

`(sin 70^circ)/(cos 20^circ) + ("cosec" 20^circ)/(sec 70^circ) - 2  cos 70^circ "cosec"  20^circ = 0`


Prove that:

`(2  "sin"  68^circ)/(cos 10^circ )- (2  cot 15^circ)/(5 tan 75^circ) = ((3  tan 45^circ t  an 20^circ  tan 40^circ tan 50^circ tan 70^circ)) /5= 1` 


Prove that:

\[\frac{\cos(90^\circ - \theta)}{1 + \sin(90^\circ - \theta)} + \frac{1 + \sin(90^\circ- \theta)}{\cos(90^\circ - \theta)} = 2 cosec\theta\]


Prove that:

\[\frac{sin\theta  \cos(90° - \theta)cos\theta}{\sin(90° - \theta)} + \frac{cos\theta  \sin(90° - \theta)sin\theta}{\cos(90° - \theta)}\]


If tan 2 A = cot (A − 12°), where 2 A is an acute angle, find the value of A.


If sec 4 A = cosec (A − 15°), where 4 A is an acute angle, find the value of A.


A man in a boat rowing away from a lighthouse 100 m high takes 2 minutes to change the angle of elevation of the top of the lighthouse from 60° to 30°. Find the speed of the boat in metres per minute [Use `sqrt3` = 1.732]


Prove the following:

`1/(1+sin^2theta) + 1/(1+cos^2theta) + 1/(1+sec^2theta) + 1/(1+cosec^2theta) = 2`


Given that `tan (θ_1 + θ_2) = (tan θ_1 + tan θ_2)/(1 - tan θ_1 tan θ_2)` Find (θ1 + θ2) when tan θ1 = `1/2 and tan θ_2 = 1/3`.


Without using tables evaluate: `(2tan 53°)/(cot 37°) - (cot 80°)/(tan 10°)`.


Solve the following equation: `(cos θ)/(1 - sin θ) + cos θ/(1 + sinθ) = 4`.


Using trigonometric table evaluate the following:
tan 25°45' + cot 45°25'.


Using trigonometric table evaluate the following:
sin 64°42' + cos 42°20'


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×