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Tense Chart || learn tense from begining || ENGLISH

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                            Tense  1 Present             2 Past               3 Future Indefinite.   Continuous.    Perfect.   Perf. Cont. अनिश्चितकालीन ,निरंतर ,पूर्ण काल ,बिल्कुल सही निरंतर काल   B) Subject {He ,she, it ,we, they, singular noun} C) Verb                                Verb Present.                 Past.              Past Participle Play                         played           Played (1st).                        (2nd).            (3rd) D)....
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trigonometric identities class 10th ncert

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TRIGONOMETRIC IDENTITY 


A trigonometric identity is an equation involving trigonometric functions that holds true for all values of the variables within its domain. There are several fundamental trigonometric identities that are widely used in mathematics. Here are some of the most common ones:

  1. Pythagorean Identity: sin^2(x) + cos^2(x) = 1 This identity relates the values of sine and cosine for any angle x in a right triangle.

  2. Reciprocal Identity: csc(x) = 1/sin(x) sec(x) = 1/cos(x) cot(x) = 1/tan(x) These identities express the reciprocals of sine, cosine, and tangent in terms of the corresponding trigonometric functions.

  3. Quotient Identity: tan(x) = sin(x)/cos(x) cot(x) = cos(x)/sin(x) These identities express tangent and cotangent in terms of sine and cosine.

  4. Co-Function Identities: sin(pi/2 - x) = cos(x) cos(pi/2 - x) = sin(x) tan(pi/2 - x) = cot(x) cot(pi/2 - x) = tan(x) These identities relate the values of trigonometric functions for complementary angles.

  5. Even-Odd Identities: sin(-x) = -sin(x) cos(-x) = cos(x) tan(-x) = -tan(x) cot(-x) = -cot(x) These identities describe the symmetry properties of trigonometric functions.

  6. Double Angle Identities: sin(2x) = 2sin(x)cos(x) cos(2x) = cos^2(x) - sin^2(x) tan(2x) = 2tan(x) / (1 - tan^2(x)) These identities express the values of trigonometric functions for double angles in terms of the values for single angles.

These are just a few examples of trigonometric identities. There are many more identities involving sum and difference of angles, half angles, and product-to-sum formulas, among others. These identities are extensively used in trigonometry and related fields to simplify expressions and solve various trigonometric equations.


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