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3 years ago

Find a numerical value of one trigonometric function of x for cscx = sinx tanx + cosx

Mathematics

1 answer:

Alex787 [66]3 years ago

6 0

Answer:

Step-by-step explanation:

we have

$cscx = sinx tanx + cosx\\\\\frac{1}{sinx}=sinx.\frac{sinx}{cosx} +cosx\\\\\frac{1}{sinx}.sinx.cosx= sinx.\frac{sinx}{cosx}.sinx.cosx+cosx.sinx.cosx\\ cosx= (sinx)^{3} +sinx.(cosx)^{2} \\cosx= sinx[(sinx)^{2}+(cosx)^{2})\\ cosx=sinx.1\\cosx=sinx\\tanx=1\\x=\frac{\pi}{4} +k\pi,k-integer.$

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Given: AD = BC and AD || BC

bearhunter [10]

Answer:

ABCD is a parallelogram.

Step-by-step explanation:

A parallelogram is a quadrilateral that has two parallel and equal pairs of opposite sides.

From the given diagram,

Given: AD = BC and AD || BC, then:

i. AB = DC (both pairs of opposite sides of a parallelogram are congruent)

ii. <ADC = < BCD and < DAB = < CBA

thus, AD || BC and AB || DC (both pairs of opposite sides of a parallelogram are parallel)

iii. < BAC = < DCA (alternate angle property)

iv. Join BD, line AC and BC are the diagonals of the quadrilateral which bisect each other. The two diagonals are at a right angle to each other.

v. <ADC + < BCD + < DAB + < CBA = $360^{0}$ (sum of angles in a quadrilateral equals 4 right angles)

Therefore, ABCD is a parallelogram.

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yKpoI14uk [10]

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Answer:

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Step-by-step explanation:

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