How i solve the introduction of trigonometry of class 10 ncert . Find the best way to solve the trigonometry question of exercise 8.4 question number 1 easily, please help me to solve the question in a easiest way.Express the trigonometric ratios sin A, sec A and tan A in terms of cot A

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To convert the given trigonometric ratios in terms of cot functions, use trigonometric formulas

We know that,

cosec

^{2}A^{ }– cot^{2}A = 1cosec

^{2}A = 1 + cot^{2}ASince cosec function is the inverse of sin function, it is written as

1/sin

^{2}A = 1 + cot^{2}ANow, rearrange the terms, it becomes

sin

^{2}A = 1/(1+cot^{2}A)Now, take square roots on both sides, we get

sin A = ±1/(√(1+cot

^{2}A)The above equation defines the sin function in terms of cot function

Now, to express sec function in terms of cot function, use this formula

sin

^{2}A = 1/ (1+cot^{2}A)Now, represent the sin function as cos function

1 – cos

^{2}A = 1/ (1+cot^{2}A)Rearrange the terms,

cos

^{2}A = 1 – 1/(1+cot^{2}A)⇒cos

^{2}A = (1-1+cot^{2}A)/(1+cot^{2}A)Since sec function is the inverse of cos function,

⇒ 1/sec

^{2}A = cot^{2}A/(1+cot^{2}A)Take the reciprocal and square roots on both sides, we get

⇒ sec A = ±√ (1+cot

^{2}A)/cotANow, to express tan function in terms of cot function

tan A = sin A/cos A and cot A = cos A/sin A

Since cot function is the inverse of tan function, it is rewritten as

tan A = 1/cot A