Ii Choose the correct option- ii 1 - tan - - sec - 1 - cot - - cosec - A 0 B 1 C 2 D -1

(ii) (C) is correct. (1 + tan θ + sec θ ) (1 + cot θ cosec θ ) = (1 + sin θ/cos θ + 1/cos θ ) (1 + cos θ/sin θ 1/sin θ ) = (cos θ + sin θ +1)/cos θ×(sin θ ...

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Standard X

Mathematics

Trigonometric Identities

ii Choose the...

Question

Question 4 (ii)
Choose the correct option.
(ii) $(1 + t a n θ + s e c θ) (1 + c o t θ - c o s e c θ)$
(A) 0
(B) 1
(C) 2
(D) -1

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Solution

(ii) (C) is correct.
$(1 + t a n θ + s e c θ) (1 + c o t θ - c o s e c θ)$
$= (1 + \frac{s i n θ}{c o s θ} + \frac{1}{c o s θ}) (1 + \frac{c o s θ}{s i n θ} - \frac{1}{s i n θ})$
$= \frac{(c o s θ + s i n θ + 1)}{c o s θ} \times \frac{(s i n θ + c o s θ - 1)}{s i n θ}$
$= \frac{(c o s θ + s i n θ)^{2} - 1^{2}}{(c o s θ s i n θ)}$
$= \frac{(c o s^{2} θ + s i n^{2} θ + 2 c o s θ s i n θ - 1)}{(c o s θ s i n θ)}$
$= \frac{(1 + 2 c o s θ s i n θ - 1)}{(c o s θ s i n θ)}$
$= \frac{(2 c o s θ s i n θ)}{(c o s θ s i n θ)} = 2$

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Similar questions

Q. Question 4 (ii)
Choose the correct option.
(ii)

(1 + t a n θ + s e c θ) (1 + c o t θ - c o s e c θ)

(A) 0
(B) 1
(C) 2
(D) -1

Choose the correct option. Justify your choice.

(i) $9 {sec}^{2} A - 9 {tan}^{2} A =$

(A) $1$

(B) $9$

(D) $0$

(ii) $(1 + tan θ + sec θ) (1 + cot θ - cosec θ)$

(A) $0$

(B) $1$

(D) $- 1$

(iii) $(sec A + tan A) (1 - sin A) =$

(A) $sec A$

(B) $sin A$

(D) $cos A$

(iv) $\frac{1 + {tan}^{2} A}{1 + {cot}^{2} A} =$

(A) ${sec}^{2} A$

(B) $- 1$

(D) ${tan}^{2} A$

Q. (1 + tan θ + sec θ) (1 + cot θ − cosec θ) =

(a) 0
(b) 1
(c) 1
(d) −1

Q. Choose the correct option. Justify your choice.

(1 + tan θ + sec θ) (1 + cot θ - c o s e c θ) = ?

Q. Choose the correct option.

(1 + t a n θ + s e c θ) (1 + c o t θ - c o s e c θ) =

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Question 4 (ii) Choose the correct option. (ii) (1+tanθ+secθ)(1+cotθ−cosecθ) (A) 0 (B) 1 (C) 2 (D) -1

(ii) (C) is correct. (1+tanθ+secθ)(1+cotθ−cosecθ) =(1+sinθcosθ+1cosθ)(1+cosθsinθ−1sinθ) =(cosθ+sinθ+1)cosθ×(sinθ+cosθ−1)sinθ =(cosθ+sinθ)2−12(cosθsinθ) =(cos2θ+sin2θ+2cosθsinθ−1)(cosθsinθ) =(1+2cosθsinθ−1)(cosθsinθ) =(2cosθsinθ)(cosθsinθ)=2

Question 4 (ii)
Choose the correct option.
(ii) $(1 + t a n θ + s e c θ) (1 + c o t θ - c o s e c θ)$
(A) 0
(B) 1
(C) 2
(D) -1