Evaluating a Trigonometric Expression In Exercises 35-40, find the exact value of the expression. 35. sin 5 cos + cos 4 12 sin 12 36. cos sin 16 16 sin cos 16 16 37. cos 130° cos 10° + sin 130° sin 10° 38. sin 100° cos 40° – cos 100° sin 40° tan(97/8) – tan(1/8) 39. 1 + tan(97/8) tan(1/8) tan 25° + tan 110° 40. 1 tan 25° tan 110°

Q: Define Lagrange Identity?

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Q: Evaluate tan- (tan()). Enter an exact answer. 3

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Q: Rewrite cot sin cot sin 1 - 1 W1 W 4+w 4 + w 2 2 as an algebraic expression in w. 0 >

A: Cot[sin-1(w/sqrt(4+w2))]

Q: cot (45°+ e) - tan ( 45°-e) %3D Prove that; 2+an 20

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Q: For Exercises 73–104, verify that the equation is an identity.

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Q: Simplify the expression dz tan sec r tan2 x -1

A: we know tan2x=sec2x-1. so in equation (sec2x-1)/(1-sec2x) = -(sec2x-1)/(sec2x-1) =-1

Q: klanah Class work% Sketen by applying the Nelson graph of transfirmattong the f u= sin Cxt IF)+z…

A: Given :     y = sin (x)  We sketch for y = sin ( x + π/4 ) +2

Q: Using trigonometric substitution

A: I=∫9+x2x3dx                                                       1---------------------put x=3tanv…

Q: tan-1(tan(6t))

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Q: Simplify the expression tan r+cot a cot a O tan? x O - tan? a O - sec2 x O sec? x

A: Options D is correct.

Trigonometric Identities

Trigonometry in mathematics deals with the right-angled triangle’s angles and sides. By trigonometric identities, we mean the identities we use whenever we need to express the various trigonometric functions in terms of an equation.

Inverse Trigonometric Functions

Inverse trigonometric functions are the inverse of normal trigonometric functions. Alternatively denoted as cyclometric or arcus functions, these inverse trigonometric functions exist to counter the basic trigonometric functions, such as sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (cosec). When trigonometric ratios are calculated, the angular values can be calculated with the help of the inverse trigonometric functions.